Showing 1–50 of 63 results for author: Vasseur, R

Statistical Mechanics of Non-Abelian Learnability Transitions

Authors: Ruochen Ma, Romain Vasseur

Abstract: Monitored many-body quantum systems can undergo sharp learnability transitions characterized by how much information can be learned by the observer. When the dynamics conserves a non-Abelian charge, such as an $SU(2)$ spin, understanding how the observer learns the total charge remains an outstanding problem. Unlike the Abelian case, where charge measurements on distinct sites commute, the… ▽ More Monitored many-body quantum systems can undergo sharp learnability transitions characterized by how much information can be learned by the observer. When the dynamics conserves a non-Abelian charge, such as an $SU(2)$ spin, understanding how the observer learns the total charge remains an outstanding problem. Unlike the Abelian case, where charge measurements on distinct sites commute, the $SU(2)$-symmetric readouts are noncommuting fusion measurements, making learning a genuinely quantum inference problem. In this work, we propose a theory of $1+1d$ monitored quantum dynamics with $SU(2)$ symmetry, and show that it can be described by an effective replicated loop model comprised of a replica-pairing field and a diffusive ($z=2$) background sector that carries the $SU(2)$ charge and remains gapless throughout the phase diagram. Our theory predicts that the "spin-sharpening'' and entanglement transitions coincide as a single transition. Ordering of the pairing field produces volume-law entanglement and hides the background sector from measurements, leading to a learning time of $t\sim L^{3}$ for the total spin. When the pairing field disorders, the background sector alone gives logarithmic entanglement and a diffusive learning time $t\sim L^{2}$. Our analysis is controlled by a large-loop-fugacity expansion. △ Less

Submitted 19 August, 2026; originally announced August 2026.

Comments: 32 pages, 3 figures

Theory of Measurement-Altered Criticality

Authors: Kabir Khanna, Sara Murciano, Romain Vasseur

Abstract: Local measurements can alter long-range correlations in gapless quantum matter. We propose a theory of weakly-monitored Tomonaga-Luttinger liquids, a broad class of quantum critical states in one dimension. In order to address the intrinsic randomness of the measurement record, we develop a replica instanton calculation to study Born-averaged observables. We find that when measurements are relevan… ▽ More Local measurements can alter long-range correlations in gapless quantum matter. We propose a theory of weakly-monitored Tomonaga-Luttinger liquids, a broad class of quantum critical states in one dimension. In order to address the intrinsic randomness of the measurement record, we develop a replica instanton calculation to study Born-averaged observables. We find that when measurements are relevant, average correlators of density and phase fluctuations decay at long distances as universal power laws with logarithmic corrections, a feature we argue is peculiar to measurement-induced randomness. We characterize the full multifractal spectrum of moments of correlations functions, revealing broad, strongly non-gaussian fluctuations across the ensemble of post-measurement states. We support these analytic results with matrix-product-state calculations, and provide a general picture of measurement-altered criticality for ground states described by 1+1d conformal field theories. Our results establish that physical measurements alter critical quantum states in a manner that lies beyond both forced measurements and conventional critical scaling. △ Less

Submitted 5 August, 2026; originally announced August 2026.

Comments: 24 pages, 6 figures

Post-selected Criticality in Measurement-induced Phase Transitions

Authors: Dolly Nambi, Kabir Khanna, Andrew Allocca, Thomas Iadecola, Ciarán Hickey, Romain Vasseur, Justin H. Wilson

Abstract: Information-theoretic phase transitions, such as the measurement-induced phase transition (MIPT), characterize the robustness of quantum dynamics to local monitoring and are naturally formulated in terms of trajectories conditioned on typical measurement outcomes, which are naively accessible only through post-selection. Here we implement forced measurements to investigate how explicit post-select… ▽ More Information-theoretic phase transitions, such as the measurement-induced phase transition (MIPT), characterize the robustness of quantum dynamics to local monitoring and are naturally formulated in terms of trajectories conditioned on typical measurement outcomes, which are naively accessible only through post-selection. Here we implement forced measurements to investigate how explicit post-selection alters the nature of the transition. We find that post-selection fundamentally alters the universality class by reweighting trajectories that are otherwise rare. In particular, we obtain a correlation-length exponent $ν\approx 2.1$ larger than that of the standard MIPT and a negative effective central charge $c_\mathrm{eff}\approx -0.4$. We also compare the post-selected MIPT to the entanglement transition of Random Tensor Networks (RTN), and demonstrate that their universality class is the same. This setup further allows time-periodic, translationally-invariant circuits with post-selected weak measurements. In both models, we find that an onsite dimension of at least 3 (qutrits but not qubits) is necessary to induce a transition. △ Less

Submitted 16 March, 2026; originally announced March 2026.

Comments: 5+2 pages, 3+5 figures

Universal monitored dynamics in multimode bosonic systems

Authors: Shivam Patel, Catherine McCarthy, Ahana Chakraborty, Jordan Huang, Thomas J. DiNapoli, Romain Vasseur, J. H. Pixley, Srivatsan Chakram

Abstract: We propose a route to study monitored many-body dynamics in multimode bosonic systems using circuit quantum electrodynamics. In this experimental setting, we construct several bosonic models comprising brickwork circuits built from beam-splitter gates, local parity measurements, and optional on-site Hubbard interactions, and diagnose their monitored dynamics via ancilla purification and a learnabi… ▽ More We propose a route to study monitored many-body dynamics in multimode bosonic systems using circuit quantum electrodynamics. In this experimental setting, we construct several bosonic models comprising brickwork circuits built from beam-splitter gates, local parity measurements, and optional on-site Hubbard interactions, and diagnose their monitored dynamics via ancilla purification and a learnability-based probe. Under parity measurements, generic gate sets exhibit behavior that is largely consistent with a conventional measurement-induced phase transition, while a special class of beam-splitter circuits shows an apparent critical-like high-measurement regime in which purification times scale linearly with system size. We show that for realistic noise, gate, and measurement rates, these signatures are observable with near-term circuit QED hardware. △ Less

Submitted 13 March, 2026; originally announced March 2026.

Les Houches lectures on random quantum circuits and monitored quantum dynamics

Authors: Romain Vasseur

Abstract: These lecture notes are based on lectures given by the author at the Les Houches 2025 summer school on "Exact Solvability and Quantum Information". The central theme of these notes is to apply the philosophy of statistical mechanics to study the dynamics of quantum information in ideal and monitored random quantum circuits -- for which an exact description of individual realizations is expected to… ▽ More These lecture notes are based on lectures given by the author at the Les Houches 2025 summer school on "Exact Solvability and Quantum Information". The central theme of these notes is to apply the philosophy of statistical mechanics to study the dynamics of quantum information in ideal and monitored random quantum circuits -- for which an exact description of individual realizations is expected to be generically intractable. △ Less

Submitted 19 February, 2026; originally announced February 2026.

Comments: 27 pages, 7 figures. Comments welcome

Strong-to-Weak Symmetry Breaking in Open Quantum Systems: From Discrete Particles to Continuum Hydrodynamics

Authors: Jacob Hauser, Kaixiang Su, Hyunsoo Ha, Jerome Lloyd, Thomas G. Kiely, Romain Vasseur, Sarang Gopalakrishnan, Cenke Xu, Matthew P. A. Fisher

Abstract: We explore the onset of spontaneous strong-to-weak symmetry breaking (SW-SSB) under U(1)-symmetric (i.e., charge-conserving) open-system dynamics. We define this phenomenon for quantum states and classical probability distributions, and explore it in three complementary models, one of which exhibits nontrivial quantum coherence at short times. Our main conclusions are as follows. In one dimension,… ▽ More We explore the onset of spontaneous strong-to-weak symmetry breaking (SW-SSB) under U(1)-symmetric (i.e., charge-conserving) open-system dynamics. We define this phenomenon for quantum states and classical probability distributions, and explore it in three complementary models, one of which exhibits nontrivial quantum coherence at short times. Our main conclusions are as follows. In one dimension, the strong symmetry is not spontaneously broken at any finite time; however, correlators probing strong-to-weak symmetry breaking develop order on length scales that grow linearly in time, parametrically faster than charge diffusion. We provide numerical evidence for this scaling in multiple distinct probes of SW-SSB, and derive it from a field-theory analysis. Moreover, we relate this scaling to the problem of inferring the charge inside a subregion by measuring its surroundings, and construct explicit decoding protocols that illustrate its origin. In two dimensions, field theory and numerical simulations support a finite-time Berezinskii-Kosterlitz-Thouless-like SW-SSB transition. Within continuum hydrodynamics, by contrast, SW-SSB happens at infinitesimal time in two or more dimensions. The SW-SSB transition time can thus be interpreted as marking the emergence of a continuum hydrodynamic description, or (more precisely) the timescale beyond which non-hydrodynamic information such as discrete particle worldlines can no longer be inferred. We support this picture by analyzing a model in which we exploit SW-SSB to derive a classical stochastic hydrodynamic description from the underlying quantum dynamics. △ Less

Submitted 17 February, 2026; originally announced February 2026.

Comments: 38+10 pages, 12+3 figures

Universal Statistics of Measurement-Induced Entanglement in Tomonaga-Luttinger liquids

Authors: Kabir Khanna, Romain Vasseur

Abstract: We study the statistics of measurement-induced entanglement (MIE) after partial measurement on a class of one-dimensional quantum critical states described by Tomonaga-Luttinger liquids at low energies. Using a replica trick to average over measurement outcomes in the charge basis and tools from conformal field theory (CFT), we derive closed-form expressions for the cumulants of MIE. We show that… ▽ More We study the statistics of measurement-induced entanglement (MIE) after partial measurement on a class of one-dimensional quantum critical states described by Tomonaga-Luttinger liquids at low energies. Using a replica trick to average over measurement outcomes in the charge basis and tools from conformal field theory (CFT), we derive closed-form expressions for the cumulants of MIE. We show that exact Born-averaging over microscopic measurement outcomes becomes equivalent at low energy to averaging over conformal boundary conditions weighted by their corresponding partition functions. Our results yield distinctive critical behavior across all cumulants in the regime where the unmeasured parts of the system are maximally separated. We also obtain the full distribution of MIE, finding that it is generically bimodal and exhibits fat-tails. We corroborate our analytical predictions by numerical calculations and find good agreement between them. △ Less

Submitted 24 June, 2026; v1 submitted 15 December, 2025; originally announced December 2025.

Comments: 34 pages, 6 figures

Learning measurement-induced phase transitions using attention

Authors: Hyejin Kim, Abhishek Kumar, Yiqing Zhou, Yichen Xu, Romain Vasseur, Eun-Ah Kim

Abstract: Measurement-induced phase transitions (MIPTs) epitomize new intellectual pursuits inspired by the advent of quantum hardware and the emergence of discrete and programmable circuit dynamics. Nevertheless, experimentally observing this transition is challenging, often requiring non-scalable protocols, such as post-selecting measurement trajectories or relying on classical simulations. We introduce a… ▽ More Measurement-induced phase transitions (MIPTs) epitomize new intellectual pursuits inspired by the advent of quantum hardware and the emergence of discrete and programmable circuit dynamics. Nevertheless, experimentally observing this transition is challenging, often requiring non-scalable protocols, such as post-selecting measurement trajectories or relying on classical simulations. We introduce a scalable data-centric approach using Quantum Attention Networks (QuAN) to detect MIPTs without requiring post-selection or classical simulation. Applying QuAN to dynamics generated by Haar random unitaries and weak measurements, we first demonstrate that it can pinpoint MIPTs using their interpretation as "learnability" transitions, where it becomes possible to distinguish two different initial states from the measurement record, locating a phase boundary consistent with exact results. Motivated by sample efficiency, we consider an alternative "phase recognition" task-classifying weak- and strong-monitoring data generated from a single initial state. We find QuAN can provide an efficient and noise-tolerant upper bound on the MIPT based on measurement data alone by coupling Born-distribution-level (inter-trajectory) and dynamical (temporal) attention. In particular, our inspection of the inter-trajectory scores of the model trained with minimal sample size processing test data confirmed that QuAN paid special attention to the tail of the distribution of the Born probabilities at early times. This reassuring interpretation of QuAN's learning implies the phase-recognition approach can meaningfully signal MIPT in an experimentally accessible manner. Our results lay the groundwork for observing MIPT on near-term quantum hardware and highlight attention-based architectures as powerful tools for learning complex quantum dynamics. △ Less

Submitted 21 August, 2025; originally announced August 2025.

Measurement-Induced Entanglement in Conformal Field Theory

Authors: Kabir Khanna, Romain Vasseur

Abstract: Local measurements can radically reshape patterns of many-body entanglement, especially in long-range entangled quantum-critical states. Yet, analytical results addressing the effects of measurements on many-body states remain scarce, and measurements are often approximated as forcing specific measurement outcomes. We study measurement-induced entanglement (MIE) in Tomonaga-Luttinger liquids, a br… ▽ More Local measurements can radically reshape patterns of many-body entanglement, especially in long-range entangled quantum-critical states. Yet, analytical results addressing the effects of measurements on many-body states remain scarce, and measurements are often approximated as forcing specific measurement outcomes. We study measurement-induced entanglement (MIE) in Tomonaga-Luttinger liquids, a broad family of 1+1d quantum critical states described at low energies by compact free boson conformal field theories (CFT). Measuring the local charge operator, we show that the MIE is entirely universal, conformally invariant, and depends on the operator content of the CFT. Using a replica-trick to address the randomness of the measurement outcomes, we compute the MIE exactly for Tomonaga-Luttinger liquids, in very good agreement with matrix-product state calculations. We show that the MIE for physical quantum measurements is fundamentally different from the entanglement induced by forcing measurement outcomes, and has a natural interpretation in terms of Born averaging over conformally-invariant boundary conditions. △ Less

Submitted 27 April, 2026; v1 submitted 4 August, 2025; originally announced August 2025.

Comments: 4.5 + 13 pages

Journal ref: Phys. Rev. Lett. 136, 160402 (2026)

Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss

Authors: Malte Pütz, Romain Vasseur, Andreas W. W. Ludwig, Simon Trebst, Guo-Yi Zhu

Abstract: In circuit-based quantum state preparation, qubit loss and coherent errors are circuit imperfections that imperil the formation of long-range entanglement beyond a certain threshold. The critical theory at the threshold is a continuous entanglement transition known to be described by a (2+0)-dimensional non-unitary conformal field theory which, for the two types of imperfections of certain circuit… ▽ More In circuit-based quantum state preparation, qubit loss and coherent errors are circuit imperfections that imperil the formation of long-range entanglement beyond a certain threshold. The critical theory at the threshold is a continuous entanglement transition known to be described by a (2+0)-dimensional non-unitary conformal field theory which, for the two types of imperfections of certain circuits, is described by either percolation or Nishimori criticality, respectively. Here we study the threshold behavior when the two types of errors simultaneously occur and show that, when moving away from the Clifford-regime of projective stabilizer measurements, the percolation critical point becomes unstable and the critical theory flows to Nishimori universality. We track this critical renormalization group (RG) crossover flow by mapping out the entanglement phase diagrams, parametrized by the probability and strength of random weak measurements, of two dual protocols preparing surface code or GHZ-class cat states from a parent cluster state via constant-depth circuits. Extensive numerical simulations, using hybrid Gaussian fermion and tensor network / Monte Carlo sampling techniques on systems with more than a million qubits, demonstrate that an infinitesimal deviation from the Clifford regime leads to a sudden, strongly non-monotonic entanglement growth at the incipient non-unitary RG flow. We argue that spectra of scaling dimensions of both the percolation and Nishimori fixed points exhibit multifractality. For percolation, we provide the exact (non-quadratic) multifractal spectrum of exponents, while for the Nishimori fixed point we show high-precision numerical results for five leading exponents characterizing multifractality. △ Less

Submitted 28 December, 2025; v1 submitted 28 May, 2025; originally announced May 2025.

Comments: 8 + 7 pages; 6 + 6 figures

Journal ref: PRX Quantum 6, 040372 (2025)

Monitored Fluctuating Hydrodynamics

Authors: Sarang Gopalakrishnan, Ewan McCulloch, Romain Vasseur

Abstract: We introduce a hydrodynamic framework for describing monitored classical stochastic processes. We study the conditional ensembles for these monitored processes -- i.e., we compute spacetime correlation functions conditioned on a fixed, typical measurement record. In the presence of global symmetries we show that these conditional ensembles can undergo measurement-induced "sharpening" phase transit… ▽ More We introduce a hydrodynamic framework for describing monitored classical stochastic processes. We study the conditional ensembles for these monitored processes -- i.e., we compute spacetime correlation functions conditioned on a fixed, typical measurement record. In the presence of global symmetries we show that these conditional ensembles can undergo measurement-induced "sharpening" phase transitions as a function of the monitoring rate; moreover, even weak monitoring can give rise to novel critical phases, derived entirely from a classical perspective. We give a simple hydrodynamic derivation of the known "charge-fuzzy phase" for weakly monitored diffusive many-body quantum systems. We show that although the unmonitored symmetric and asymmetric exclusion processes are in different universality classes of transport, the fluctuations in their conditional ensembles flow to the same fixed point with emergent relativistic invariance under monitoring. On the other hand, weakly monitored systems with non-Abelian symmetries enter a novel strongly coupled fixed point with non-trivial dynamical exponent, which we characterize. Our formalism naturally accounts for monitoring general observables, such as currents or density gradients, and allows for a direct calculation of information-theoretic diagnostics of sharpening transitions, including the Shannon entropy of the measurement record. △ Less

Submitted 14 January, 2026; v1 submitted 3 April, 2025; originally announced April 2025.

Comments: 14 pages, 4 figures

Journal ref: Phys. Rev. X 16, 011024 (2026)

Tensor Cross Interpolation of Purities in Quantum Many-Body Systems

Authors: Dmytro Kolisnyk, Raimel A. Medina, Romain Vasseur, Maksym Serbyn

Abstract: A defining feature of quantum many-body systems is the exponential scaling of the Hilbert space with the number of degrees of freedom. This exponential complexity naïvely renders a complete state characterization, for instance via the complete set of bipartite Renyi entropies for all disjoint regions, a challenging task. Recently, a compact way of storing subregions' purities by encoding them as a… ▽ More A defining feature of quantum many-body systems is the exponential scaling of the Hilbert space with the number of degrees of freedom. This exponential complexity naïvely renders a complete state characterization, for instance via the complete set of bipartite Renyi entropies for all disjoint regions, a challenging task. Recently, a compact way of storing subregions' purities by encoding them as amplitudes of a fictitious quantum wave function, known as entanglement feature, was proposed. Notably, the entanglement feature can be a simple object even for highly entangled quantum states. However the complexity and practical usage of the entanglement feature for general quantum states has not been explored. In this work, we demonstrate that the entanglement feature can be efficiently learned using only a polynomial amount of samples in the number of degrees of freedom through the so-called tensor cross interpolation (TCI) algorithm, assuming it is expressible as a finite bond dimension MPS. We benchmark this learning process on Haar and random MPS states, confirming analytic expectations. Applying the TCI algorithm to quantum eigenstates of various one dimensional quantum systems, we identify cases where eigenstates have entanglement feature learnable with TCI. We conclude with possible applications of the learned entanglement feature, such as quantifying the distance between different entanglement patterns and finding the optimal one-dimensional ordering of physical indices in a given state, highlighting the potential utility of the proposed purity interpolation method. △ Less

Submitted 15 May, 2026; v1 submitted 21 March, 2025; originally announced March 2025.

Comments: 14+6 pages, 8+3 figures, expanded discussion

Journal ref: Quantum 10, 2114 (2026)

Mixed-state learnability transitions in monitored noisy quantum dynamics

Authors: Hansveer Singh, Romain Vasseur, Andrew C. Potter, Sarang Gopalakrishnan

Abstract: We consider learnability transitions in monitored quantum systems that undergo noisy evolution, subject to a global strong symmetry -- i.e., in addition to the measuring apparatus, the system can interact with an unobserved environment, but does not exchange charge with it. As in the pure-state setting, we find two information-theoretic phases -- a sharp (fuzzy) phase in which an eavesdropper can… ▽ More We consider learnability transitions in monitored quantum systems that undergo noisy evolution, subject to a global strong symmetry -- i.e., in addition to the measuring apparatus, the system can interact with an unobserved environment, but does not exchange charge with it. As in the pure-state setting, we find two information-theoretic phases -- a sharp (fuzzy) phase in which an eavesdropper can rapidly (slowly) learn the symmetry charge. However, because the dynamics is noisy, both phases can be simulated efficiently using tensor networks. Indeed, even when the true dynamics is unitary, introducing noise by hand allows an eavesdropper to efficiently learn the symmetry charge from local measurements, as we demonstrate. We identify the fuzzy phase in this setting as a mixed-state phase that exhibits spontaneous strong-to-weak symmetry breaking. △ Less

Submitted 13 March, 2025; originally announced March 2025.

Comments: 5+epsilon pages+references, 3 figures

Journal ref: Phys. Rev. B 113, 054305 (2026)

Decoherence-induced self-dual criticality in topological states of matter

Authors: Qingyuan Wang, Romain Vasseur, Simon Trebst, Andreas W. W. Ludwig, Guo-Yi Zhu

Abstract: Quantum measurements performed on a subsystem of a quantum many-body state can generate entanglement for its remaining constituents. The whole system including the measurement record is described by a hybrid mixed state, which can exhibit exotic phase transitions and critical phenomena. We demonstrate that generic measurement-induced phase transitions (MIPTs) can be cast as decoherence-induced cri… ▽ More Quantum measurements performed on a subsystem of a quantum many-body state can generate entanglement for its remaining constituents. The whole system including the measurement record is described by a hybrid mixed state, which can exhibit exotic phase transitions and critical phenomena. We demonstrate that generic measurement-induced phase transitions (MIPTs) can be cast as decoherence-induced critical mixed states in one higher dimension, by constructing a projected entangled pair state (PEPS) prior to decoherence or measurement. In this context, a deeper conceptual understanding of such mixed-state criticality is called for, particularly with regard to algebraic symmetry as an advanced organizing principle for such entangled states of matter. Integrating these connections we investigate the role of self-dual symmetry -- a fundamental notion in theoretical physics -- in mixed states, showing that the decoherence of electric (e) and magnetic (m) vortices from the 2D bulk of the toric code, or equivalently, a 2D cluster state with symmetry-protected topological order, can leave a (1+1)D quantum critical mixed state protected by a weak Kramers-Wannier self-dual symmetry. The corresponding self-dual critical bulk is described by the N->1 limit of the 2D Non-linear Sigma Model in symmetry class D with target space SO(2N)/U(N) at $Θ$-angle $π$, and represents a "measurement-version" of the Cho-Fisher network model subjected to Born-rule randomness... △ Less

Submitted 30 December, 2025; v1 submitted 19 February, 2025; originally announced February 2025.

Comments: major revision + 6 new figs + toric code with coherent error (26 + 10 pages, 12 + 6 figures)

Random Quantum Circuits with Time-Reversal Symmetry

Authors: Kabir Khanna, Abhishek Kumar, Romain Vasseur, Andreas W. W. Ludwig

Abstract: Time-reversal (TR) symmetry is crucial for understanding a wide range of physical phenomena, and plays a key role in constraining fundamental particle interactions and in classifying phases of quantum matter. In this work, we introduce an ensemble of random quantum circuits that are representative of the dynamics of generic TR-invariant many-body quantum systems. We derive a general statistical me… ▽ More Time-reversal (TR) symmetry is crucial for understanding a wide range of physical phenomena, and plays a key role in constraining fundamental particle interactions and in classifying phases of quantum matter. In this work, we introduce an ensemble of random quantum circuits that are representative of the dynamics of generic TR-invariant many-body quantum systems. We derive a general statistical mechanics model describing entanglement, many-body quantum chaos and quantum information dynamics in such TR-invariant circuits. As an example of application of our formalism, we study the universal properties of measurement-induced phase transitions (MIPT) in monitored TR-invariant systems, with measurements performed in a TR-invariant basis. We find that TR-invariance of the unitary part of the dynamics does not affect the universality class, unless measurement outcomes are post-selected to satisfy the global TR-invariance of each quantum trajectory. We confirm these predictions numerically, and find, for both generic and Clifford-based evolutions, novel critical exponents in the case of ``strong'', i.e. global TR-invariance where each quantum trajectory is TR-invariant. △ Less

Submitted 20 March, 2026; v1 submitted 22 January, 2025; originally announced January 2025.

Comments: 24 pages, 9 figures

Journal ref: Phys. Rev. Research 8, 013165, 2026

Superdiffusive transport in chaotic quantum systems with nodal interactions

Authors: Yu-Peng Wang, Jie Ren, Sarang Gopalakrishnan, Romain Vasseur

Abstract: We introduce a class of interacting fermionic quantum models in $d$ dimensions with nodal interactions that exhibit superdiffusive transport. We establish non-perturbatively that the nodal structure of the interactions gives rise to long-lived quasiparticle excitations that result in a diverging diffusion constant, even though the system is fully chaotic. Using a Boltzmann equation approach, we fi… ▽ More We introduce a class of interacting fermionic quantum models in $d$ dimensions with nodal interactions that exhibit superdiffusive transport. We establish non-perturbatively that the nodal structure of the interactions gives rise to long-lived quasiparticle excitations that result in a diverging diffusion constant, even though the system is fully chaotic. Using a Boltzmann equation approach, we find that the charge mode acquires an anomalous dispersion relation at long wavelength $ω(q) \sim q^{z} $ with dynamical exponent $z={\rm min}[(2n+d)/2n,2]$, where $n$ is the order of the nodal point in momentum space. We verify our predictions in one dimensional systems using tensor-network techniques. △ Less

Submitted 24 September, 2025; v1 submitted 14 January, 2025; originally announced January 2025.

Comments: 10 pages, 2 figures

Journal ref: Phys. Rev. Lett. 135, 166303(2025)

Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains

Authors: Kazumasa A. Takeuchi, Kazuaki Takasan, Ofer Busani, Patrik L. Ferrari, Romain Vasseur, Jacopo De Nardis

Abstract: Integrable spin chains with a continuous non-Abelian symmetry, such as the one-dimensional isotropic Heisenberg model, show superdiffusive transport with little theoretical understanding. Although recent studies reported a surprising connection to the Kardar-Parisi-Zhang (KPZ) universality class in that case, this view was most recently questioned by discrepancies in full counting statistics. Here… ▽ More Integrable spin chains with a continuous non-Abelian symmetry, such as the one-dimensional isotropic Heisenberg model, show superdiffusive transport with little theoretical understanding. Although recent studies reported a surprising connection to the Kardar-Parisi-Zhang (KPZ) universality class in that case, this view was most recently questioned by discrepancies in full counting statistics. Here, by combining extensive numerical simulations of classical and quantum integrable isotropic spin chains with a framework developed by exact studies of the KPZ class, we characterize various two-point quantities that remain hitherto unexplored in spin chains, and find full agreement with KPZ scaling laws without adjustable parameters. This establishes the partial emergence of the KPZ class in integrable isotropic spin chains. Moreover, we reveal that the KPZ scaling laws are intact in the presence of an energy current, under the appropriate Galilean boost required by the propagation of spacetime correlation. △ Less

Submitted 6 March, 2025; v1 submitted 11 June, 2024; originally announced June 2024.

Comments: 8+6 pages, 6+2 figures, 1 table

Journal ref: Phys. Rev. Lett. 134, 097104 (2025)

Emergence of Navier-Stokes hydrodynamics in chaotic quantum circuits

Authors: Hansveer Singh, Ewan McCulloch, Sarang Gopalakrishnan, Romain Vasseur

Abstract: We construct an ensemble of two-dimensional nonintegrable quantum circuits that are chaotic but have a conserved particle current, and thus a finite Drude weight. The long-wavelength hydrodynamics of such systems is given by the incompressible Navier-Stokes equations. By analyzing circuit-to-circuit fluctuations in the ensemble we argue that these are negligible, so the circuit-averaged value of t… ▽ More We construct an ensemble of two-dimensional nonintegrable quantum circuits that are chaotic but have a conserved particle current, and thus a finite Drude weight. The long-wavelength hydrodynamics of such systems is given by the incompressible Navier-Stokes equations. By analyzing circuit-to-circuit fluctuations in the ensemble we argue that these are negligible, so the circuit-averaged value of transport coefficients like the viscosity is also (in the long-time limit) the value in a typical circuit. The circuit-averaged transport coefficients can be mapped onto a classical irreversible Markov process. Therefore, remarkably, our construction allows us to efficiently compute the viscosity of a family of strongly interacting chaotic two-dimensional quantum systems. △ Less

Submitted 22 May, 2024; originally announced May 2024.

Comments: 4+epsilon pages, 3 figures; 8 pages supplemental material

Journal ref: Phys. Rev. Lett. 134, 230401 (2025)

Non-Gaussian diffusive fluctuations in Dirac fluids

Authors: Sarang Gopalakrishnan, Ewan McCulloch, Romain Vasseur

Abstract: Dirac fluids - interacting systems obeying particle-hole symmetry and Lorentz invariance - are among the simplest hydrodynamic systems; they have also been studied as effective descriptions of transport in strongly interacting Dirac semimetals. Direct experimental signatures of the Dirac fluid are elusive, as its charge transport is diffusive as in conventional metals. In this paper we point out a… ▽ More Dirac fluids - interacting systems obeying particle-hole symmetry and Lorentz invariance - are among the simplest hydrodynamic systems; they have also been studied as effective descriptions of transport in strongly interacting Dirac semimetals. Direct experimental signatures of the Dirac fluid are elusive, as its charge transport is diffusive as in conventional metals. In this paper we point out a striking consequence of fluctuating relativistic hydrodynamics: the full counting statistics (FCS) of charge transport is highly non-gaussian. We predict the exact asymptotic form of the FCS, which generalizes a result previously derived for certain interacting integrable systems. A consequence is that, starting from quasi-one dimensional nonequilibrium initial conditions, charge noise in the hydrodynamic regime is parametrically enhanced relative to that in conventional diffusive metals. △ Less

Submitted 10 January, 2024; originally announced January 2024.

Comments: 5 pages, 2 figures

Journal ref: Proceedings of the National Academy of Sciences, 121 (50) e2403327121 (2024)

Universal structure of measurement-induced information in many-body ground states

Authors: Zihan Cheng, Rui Wen, Sarang Gopalakrishnan, Romain Vasseur, Andrew C. Potter

Abstract: Unlike unitary dynamics, measurements of a subsystem can induce long-range entanglement via quantum teleportation. The amount of measurement-induced entanglement or mutual information depends jointly on the measurement basis and the entanglement structure of the state (before measurement), and has operational significance for whether the state is a resource for measurement-based quantum computing,… ▽ More Unlike unitary dynamics, measurements of a subsystem can induce long-range entanglement via quantum teleportation. The amount of measurement-induced entanglement or mutual information depends jointly on the measurement basis and the entanglement structure of the state (before measurement), and has operational significance for whether the state is a resource for measurement-based quantum computing, as well as for the computational complexity of simulating the state using quantum or classical computers. In this work, we examine entropic measures of measurement-induced entanglement (MIE) and information (MII) for the ground-states of quantum many-body systems in one- and two- spatial dimensions. From numerical and analytic analysis of a variety of models encompassing critical points, quantum Hall states, string-net topological orders, and Fermi liquids, we identify universal features of the long-distance structure of MIE and MII that depend only on the underlying phase or critical universality class of the state. We argue that, whereas in $1d$ the leading contributions to long-range MIE and MII are universal, in $2d$, the existence of a teleportation transition for finite-depth circuits implies that trivial $2d$ states can exhibit long-range MIE, and the universal features lie in sub-leading corrections. We introduce modified MIE measures that directly extract these universal contributions. As a corollary, we show that the leading contributions to strange-correlators, used to numerically identify topological phases, are in fact non-universal in two or more dimensions, and explain how our modified constructions enable one to isolate universal components. We discuss the implications of these results for classical- and quantum- computational simulation of quantum materials. △ Less

Submitted 8 May, 2024; v1 submitted 18 December, 2023; originally announced December 2023.

Comments: 14+2 pages, 10+1 figures; v2: published version, added DMRG simulation for the XXZ model

Journal ref: Phys. Rev. B 109, 195128 (2024)

Generalized hydrodynamics: a perspective

Authors: Benjamin Doyon, Sarang Gopalakrishnan, Frederik Møller, Jörg Schmiedmayer, Romain Vasseur

Abstract: Conventional hydrodynamics describes systems with few long-lived excitations. In one dimension, however, many experimentally relevant systems feature a large number of long-lived excitations even at high temperature, because they are proximate to integrable limits. Such models cannot be treated using conventional hydrodynamics. The framework of generalized hydrodynamics (GHD) was recently develope… ▽ More Conventional hydrodynamics describes systems with few long-lived excitations. In one dimension, however, many experimentally relevant systems feature a large number of long-lived excitations even at high temperature, because they are proximate to integrable limits. Such models cannot be treated using conventional hydrodynamics. The framework of generalized hydrodynamics (GHD) was recently developed to treat the dynamics of one-dimensional models: it combines ideas from integrability, hydrodynamics, and kinetic theory to come up with a quantitative theory of transport. GHD has successfully settled several longstanding questions about one-dimensional transport; it has also been leveraged to study dynamical questions beyond the transport of conserved quantities, and to systems that are not integrable. In this article we introduce the main ideas and predictions of GHD, survey some of the most recent theoretical extensions and experimental tests of the GHD framework, and discuss some open questions in transport that the GHD perspective might elucidate. △ Less

Submitted 6 November, 2023; originally announced November 2023.

Comments: 16 pages, 5 figures, perspective article, feedback is welcome

Journal ref: Phys. Rev. X 15, 010501 (2025)

Observing quantum measurement collapse as a learnability phase transition

Authors: Utkarsh Agrawal, Javier Lopez-Piqueres, Romain Vasseur, Sarang Gopalakrishnan, Andrew C. Potter

Abstract: The mechanism by which an effective macroscopic description of quantum measurement in terms of discrete, probabilistic collapse events emerges from the reversible microscopic dynamics remains an enduring open question. Emerging quantum computers offer a promising platform to explore how measurement processes evolve across a range of system sizes while retaining coherence. Here, we report the exper… ▽ More The mechanism by which an effective macroscopic description of quantum measurement in terms of discrete, probabilistic collapse events emerges from the reversible microscopic dynamics remains an enduring open question. Emerging quantum computers offer a promising platform to explore how measurement processes evolve across a range of system sizes while retaining coherence. Here, we report the experimental observation of evidence for an observable-sharpening measurement-induced phase transition in a chain of trapped ions in Quantinuum H1-1 system model quantum processor. This transition manifests as a sharp, concomitant change in both the quantum uncertainty of an observable and the amount of information an observer can (in principle) learn from the measurement record, upon increasing the strength of measurements. We leverage insights from statistical mechanical models and machine learning to design efficiently-computable algorithms to observe this transition (without non-scalable post-selection on measurement outcomes) and to mitigate the effects on errors in noisy hardware. △ Less

Submitted 31 October, 2023; originally announced November 2023.

Journal ref: Phys. Rev. X 14, 041012 (2024)

Boundary transfer matrix spectrum of measurement-induced transitions

Authors: Abhishek Kumar, Kemal Aziz, Ahana Chakraborty, Andreas W. W. Ludwig, Sarang Gopalakrishnan, J. H. Pixley, Romain Vasseur

Abstract: Measurement-induced phase transitions (MIPTs) are known to be described by non-unitary conformal field theories (CFTs) whose precise nature remains unknown. Most physical quantities of interest, such as the entanglement features of quantum trajectories, are described by boundary observables in this CFT. We introduce a transfer matrix approach to study the boundary spectrum of this field theory, an… ▽ More Measurement-induced phase transitions (MIPTs) are known to be described by non-unitary conformal field theories (CFTs) whose precise nature remains unknown. Most physical quantities of interest, such as the entanglement features of quantum trajectories, are described by boundary observables in this CFT. We introduce a transfer matrix approach to study the boundary spectrum of this field theory, and consider a variety of boundary conditions. We apply this approach numerically to monitored Haar and Clifford circuits, and to the measurement-only Ising model where the boundary scaling dimensions can be derived analytically. Our transfer matrix approach provides a systematic numerical tool to study the spectrum of MIPTs. △ Less

Submitted 5 January, 2024; v1 submitted 4 October, 2023; originally announced October 2023.

Comments: 17 pages, 12 figures, 1 table

Journal ref: Phys. Rev. B 109, 014303 (2024)

Measurement induced criticality in quasiperiodic modulated random hybrid circuits

Authors: Gal Shkolnik, Aidan Zabalo, Romain Vasseur, David A. Huse, J. H. Pixley, Snir Gazit

Abstract: We study one-dimensional hybrid quantum circuits perturbed by quenched quasiperiodic (QP) modulations across the measurement-induced phase transition (MIPT). Considering non-Pisot QP structures, characterized by unbounded fluctuations, allows us to tune the wandering exponent $β$ to exceed the Luck bound $ν\ge 1/(1-β)$ for the stability of the MIPT, where $ν=1.28(2)$. Via robust numerical simulati… ▽ More We study one-dimensional hybrid quantum circuits perturbed by quenched quasiperiodic (QP) modulations across the measurement-induced phase transition (MIPT). Considering non-Pisot QP structures, characterized by unbounded fluctuations, allows us to tune the wandering exponent $β$ to exceed the Luck bound $ν\ge 1/(1-β)$ for the stability of the MIPT, where $ν=1.28(2)$. Via robust numerical simulations of random Clifford circuits interleaved with local projective measurements, we find that sufficiently large QP structural fluctuations destabilize the MIPT and induce a flow to a broad family of critical dynamical phase transitions of the infinite QP type that is governed by the wandering exponent, $β$. We numerically determine the associated critical properties, including the correlation length exponent consistent with saturating the Luck bound, and a universal activated dynamical scaling with activation exponent $ψ\cong β$, finding excellent agreement with the conclusions of real space renormalization group calculations. △ Less

Submitted 25 June, 2024; v1 submitted 7 August, 2023; originally announced August 2023.

Comments: 14 pages, 13 figures

Journal ref: Phys. Rev. B 108, 184204 (2023)

Random insights into the complexity of two-dimensional tensor network calculations

Authors: Sofia Gonzalez-Garcia, Shengqi Sang, Timothy H. Hsieh, Sergio Boixo, Guifre Vidal, Andrew C. Potter, Romain Vasseur

Abstract: Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law, and are the basis for classical simulations of ground states in two-dimensional (2d) condensed matter systems. However, rigorous results show that exactly computing observables from a 2d PEPS state is generically a computationally hard problem. Yet appr… ▽ More Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law, and are the basis for classical simulations of ground states in two-dimensional (2d) condensed matter systems. However, rigorous results show that exactly computing observables from a 2d PEPS state is generically a computationally hard problem. Yet approximation schemes for computing properties of 2d PEPS are regularly used, and empirically seen to succeed, for a large subclass of (not too entangled) condensed matter ground states. Adopting the philosophy of random matrix theory, in this work we analyze the complexity of approximately contracting a 2d random PEPS by exploiting an analytic mapping to an effective replicated statistical mechanics model that permits a controlled analysis at large bond dimension. Through this statistical-mechanics lens, we argue that: i) although approximately sampling wave-function amplitudes of random PEPS faces a computational-complexity phase transition above a critical bond dimension, ii) one can generically efficiently estimate the norm and correlation functions for any finite bond dimension. These results are supported numerically for various bond-dimension regimes. It is an important open question whether the above results for random PEPS apply more generally also to PEPS representing physically relevant ground states △ Less

Submitted 20 July, 2023; originally announced July 2023.

Journal ref: Phys. Rev. B 109, 235102 (2024)

Emergence of fluctuating hydrodynamics in chaotic quantum systems

Authors: Julian F. Wienand, Simon Karch, Alexander Impertro, Christian Schweizer, Ewan McCulloch, Romain Vasseur, Sarang Gopalakrishnan, Monika Aidelsburger, Immanuel Bloch

Abstract: A fundamental principle of chaotic quantum dynamics is that local subsystems eventually approach a thermal equilibrium state. Large subsystems thermalize slower: their approach to equilibrium is limited by the hydrodynamic build-up of large-scale fluctuations. For classical out-of-equilibrium systems, the framework of macroscopic fluctuation theory (MFT) was recently developed to model the hydrody… ▽ More A fundamental principle of chaotic quantum dynamics is that local subsystems eventually approach a thermal equilibrium state. Large subsystems thermalize slower: their approach to equilibrium is limited by the hydrodynamic build-up of large-scale fluctuations. For classical out-of-equilibrium systems, the framework of macroscopic fluctuation theory (MFT) was recently developed to model the hydrodynamics of fluctuations. We perform large-scale quantum simulations that monitor the full counting statistics of particle-number fluctuations in hard-core boson ladders, contrasting systems with ballistic and chaotic dynamics. We find excellent agreement between our results and MFT predictions, which allows us to accurately extract diffusion constants from fluctuation growth. Our results suggest that large-scale fluctuations of isolated quantum systems display emergent hydrodynamic behavior, expanding the applicability of MFT to the quantum regime. △ Less

Submitted 20 June, 2023; originally announced June 2023.

Journal ref: Nature Physics 20, 1732-1737 (2024)

Tunable superdiffusion in integrable spin chains using correlated initial states

Authors: Hansveer Singh, Michael H. Kolodrubetz, Sarang Gopalakrishnan, Romain Vasseur

Abstract: Although integrable spin chains only host ballistically propagating particles they can still feature diffusive spin transport. This diffusive spin transport originates from quasiparticle charge fluctuations inherited from the initial state's magnetization Gaussian fluctuations. We show that ensembles of initial states with quasi-long range correlations lead to superdiffusive spin transport with a… ▽ More Although integrable spin chains only host ballistically propagating particles they can still feature diffusive spin transport. This diffusive spin transport originates from quasiparticle charge fluctuations inherited from the initial state's magnetization Gaussian fluctuations. We show that ensembles of initial states with quasi-long range correlations lead to superdiffusive spin transport with a tunable dynamical exponent. We substantiate our prediction with numerical simulations and explain how deviations arise from finite time and finite size effects. △ Less

Submitted 7 June, 2023; originally announced June 2023.

Comments: 4+epsilon pages, 3 figures; Comments welcome

Journal ref: Phys. Rev. Lett. 132, 176303 (2024)

Quantum turnstiles for robust measurement of full counting statistics

Authors: Rhine Samajdar, Ewan McCulloch, Vedika Khemani, Romain Vasseur, Sarang Gopalakrishnan

Abstract: We present a scalable protocol for measuring full counting statistics (FCS) in experiments or tensor-network simulations. In this method, an ancilla in the middle of the system acts as a turnstile, with its phase keeping track of the time-integrated particle flux. Unlike quantum gas microscopy, the turnstile protocol faithfully captures FCS starting from number-indefinite initial states or in the… ▽ More We present a scalable protocol for measuring full counting statistics (FCS) in experiments or tensor-network simulations. In this method, an ancilla in the middle of the system acts as a turnstile, with its phase keeping track of the time-integrated particle flux. Unlike quantum gas microscopy, the turnstile protocol faithfully captures FCS starting from number-indefinite initial states or in the presence of noisy dynamics. In addition, by mapping the FCS onto a single-body observable, it allows for stable numerical calculations of FCS using approximate tensor-network methods. We demonstrate the wide-ranging utility of this approach by computing the FCS of the transferred magnetization in a Floquet Heisenberg spin chain, as studied in a recent experiment with superconducting qubits, as well as the FCS of charge transfer in random circuits. △ Less

Submitted 24 May, 2023; originally announced May 2023.

Comments: 8+3 pages, 4+4 figures

Journal ref: Phys. Rev. Lett. 133, 240403 (2024)

Superdiffusion from nonabelian symmetries in nearly integrable systems

Authors: Sarang Gopalakrishnan, Romain Vasseur

Abstract: The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is sub-ballistic at any nonzero temperature: an initially localized spin fluctuation spreads in time $t$ to a width $t^{2/3}$. This exponent, as well as the functional form of the dynamical spin correlation function, suggest that spin transport is in t… ▽ More The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is sub-ballistic at any nonzero temperature: an initially localized spin fluctuation spreads in time $t$ to a width $t^{2/3}$. This exponent, as well as the functional form of the dynamical spin correlation function, suggest that spin transport is in the Kardar-Parisi-Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry, and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry. △ Less

Submitted 24 May, 2023; originally announced May 2023.

Comments: review article, 17 pages + refs. Comments welcome

Journal ref: Annual Review of Condensed Matter Physics Vol. 15:159-176 (2024)

Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits

Authors: Shayan Majidy, Utkarsh Agrawal, Sarang Gopalakrishnan, Andrew C. Potter, Romain Vasseur, Nicole Yunger Halpern

Abstract: Monitored quantum circuits exhibit entanglement transitions at certain measurement rates. Such a transition separates phases characterized by how much information an observer can learn from the measurement outcomes. We study SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping onto an effective statistical-mechanics model. Due to the symmetry's non-Abelian nature, measuri… ▽ More Monitored quantum circuits exhibit entanglement transitions at certain measurement rates. Such a transition separates phases characterized by how much information an observer can learn from the measurement outcomes. We study SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping onto an effective statistical-mechanics model. Due to the symmetry's non-Abelian nature, measuring qubit pairs allows for nontrivial entanglement scaling even in the measurement-only limit. We find a transition between a volume-law entangled phase and a critical phase whose diffusive purification dynamics emerge from the non-Abelian symmetry. Additionally, we numerically identify a "spin-sharpening transition." On one side is a phase in which the measurements can efficiently identify the system's total spin quantum number; on the other side is a phase in which measurements cannot. △ Less

Submitted 19 August, 2023; v1 submitted 22 May, 2023; originally announced May 2023.

Comments: 8 pages (6 figures) + appendices (11.5 pages)

Journal ref: Phys. Rev. B 108, 054307 (2023)

Full Counting Statistics of Charge in Chaotic Many-body Quantum Systems

Authors: Ewan McCulloch, Jacopo De Nardis, Sarang Gopalakrishnan, Romain Vasseur

Abstract: We investigate the full counting statistics of charge transport in $U(1)$-symmetric random unitary circuits. We consider an initial mixed state prepared with a chemical potential imbalance between the left and right halves of the system, and study the fluctuations of the charge transferred across the central bond in typical circuits. Using an effective replica statistical mechanics model and a map… ▽ More We investigate the full counting statistics of charge transport in $U(1)$-symmetric random unitary circuits. We consider an initial mixed state prepared with a chemical potential imbalance between the left and right halves of the system, and study the fluctuations of the charge transferred across the central bond in typical circuits. Using an effective replica statistical mechanics model and a mapping onto an emergent classical stochastic process valid at large onsite Hilbert space dimension, we show that charge transfer fluctuations approach those of the symmetric exclusion process at long times, with subleading $t^{-1/2}$ quantum corrections. We discuss our results in the context of fluctuating hydrodynamics and macroscopic fluctuation theory of classical non-equilibrium systems, and check our predictions against direct matrix-product state calculations. △ Less

Submitted 1 December, 2023; v1 submitted 2 February, 2023; originally announced February 2023.

Comments: 5 pages, 2 figures, 9 page supplementary

Journal ref: Phys. Rev. Lett. 131, 210402 (2023)

Triviality of quantum trajectories close to a directed percolation transition

Authors: Lorenzo Piroli, Yaodong Li, Romain Vasseur, Adam Nahum

Abstract: We study quantum circuits consisting of unitary gates, projective measurements, and control operations that steer the system towards a pure absorbing state. Two types of phase transition occur as the rate of these control operations is increased: a measurement-induced entanglement transition, and a directed percolation transition into the absorbing state (taken here to be a product state). In this… ▽ More We study quantum circuits consisting of unitary gates, projective measurements, and control operations that steer the system towards a pure absorbing state. Two types of phase transition occur as the rate of these control operations is increased: a measurement-induced entanglement transition, and a directed percolation transition into the absorbing state (taken here to be a product state). In this work we show analytically that these transitions are generically distinct, with the quantum trajectories becoming disentangled before the absorbing state transition is reached, and we analyze their critical properties. We introduce a simple class of models where the measurements in each quantum trajectory define an Effective Tensor Network (ETN) -- a subgraph of the initial spacetime graph where nontrivial time evolution takes place. By analyzing the entanglement properties of the ETN, we show that the entanglement and absorbing-state transitions coincide only in the limit of infinite local Hilbert-space dimension. Focusing on a Clifford model which allows numerical simulations for large system sizes, we verify our predictions and study the finite-size crossover between the two transitions at large local Hilbert space dimension. We give evidence that the entanglement transition is governed by the same fixed point as in hybrid circuits without feedback. △ Less

Submitted 3 June, 2023; v1 submitted 28 December, 2022; originally announced December 2022.

Comments: 18 pages, 9 figures; v2: Appendix added, minor revision

Journal ref: Phys. Rev. B 107, 224303 (2023)

Transitions in the learnability of global charges from local measurements

Authors: Fergus Barratt, Utkarsh Agrawal, Andrew C. Potter, Sarang Gopalakrishnan, Romain Vasseur

Abstract: We consider monitored quantum systems with a global conserved charge, and ask how efficiently an observer ("eavesdropper") can learn the global charge of such systems from local projective measurements. We find phase transitions as a function of the measurement rate, depending on how much information about the quantum dynamics the eavesdropper has access to. For random unitary circuits with U(1) s… ▽ More We consider monitored quantum systems with a global conserved charge, and ask how efficiently an observer ("eavesdropper") can learn the global charge of such systems from local projective measurements. We find phase transitions as a function of the measurement rate, depending on how much information about the quantum dynamics the eavesdropper has access to. For random unitary circuits with U(1) symmetry, we present an optimal classical classifier to reconstruct the global charge from local measurement outcomes only. We demonstrate the existence of phase transitions in the performance of this classifier in the thermodynamic limit. We also study numerically improved classifiers by including some knowledge about the unitary gates pattern. △ Less

Submitted 8 July, 2022; v1 submitted 24 June, 2022; originally announced June 2022.

Journal ref: Phys. Rev. Lett. 129, 200602 (2022)

Infinite-randomness criticality in monitored quantum dynamics with static disorder

Authors: Aidan Zabalo, Justin H. Wilson, Michael J. Gullans, Romain Vasseur, Sarang Gopalakrishnan, David A. Huse, J. H. Pixley

Abstract: We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in their entanglement structure, but the nature of the critical point differs drastically from the case with constant measurement rate. In particular, at the critical… ▽ More We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in their entanglement structure, but the nature of the critical point differs drastically from the case with constant measurement rate. In particular, at the critical measurement rate, we find that the entanglement of a subsystem of size $\ell$ scales as $S \sim \sqrt{\ell}$; moreover, the dynamical critical exponent $z = \infty$. The MIPT is flanked by Griffiths phases with continuously varying dynamical exponents. We argue for this infinite-randomness scenario on general grounds and present numerical evidence that it captures some features of the universal critical properties of MIPT using large-scale simulations of Clifford circuits. These findings demonstrate that the relevance and irrelevance of perturbations to the MIPT can naturally be interpreted using a powerful heuristic known as the Harris criterion. △ Less

Submitted 27 May, 2022; originally announced May 2022.

Comments: (7 + 7) pages, (3 + 5) figures, (0 + 1) tables

Journal ref: Phys. Rev. B 107, L220204 (2023)

The Fredkin staircase: An integrable system with a finite-frequency Drude peak

Authors: Hansveer Singh, Romain Vasseur, Sarang Gopalakrishnan

Abstract: We introduce and explore an interacting integrable cellular automaton, the Fredkin staircase, that lies outside the existing classification of such automata, and has a structure that seems to lie beyond that of any existing Bethe-solvable model. The Fredkin staircase has two families of ballistically propagating quasiparticles, each with infinitely many species. Despite the presence of ballistic q… ▽ More We introduce and explore an interacting integrable cellular automaton, the Fredkin staircase, that lies outside the existing classification of such automata, and has a structure that seems to lie beyond that of any existing Bethe-solvable model. The Fredkin staircase has two families of ballistically propagating quasiparticles, each with infinitely many species. Despite the presence of ballistic quasiparticles, charge transport is diffusive in the d.c. limit, albeit with a highly non-gaussian dynamic structure factor. Remarkably, this model exhibits persistent temporal oscillations of the current, leading to a delta-function singularity (Drude peak) in the a.c. conductivity at nonzero frequency. We analytically construct an extensive set of operators that anticommute with the time-evolution operator; the existence of these operators both demonstrates the integrability of the model and allows us to lower-bound the weight of this finite-frequency singularity. △ Less

Submitted 17 May, 2022; originally announced May 2022.

Comments: 4.5 pages, 3 figures plus 9 pages supplemental material

Journal ref: Phys. Rev. Lett. 130, 046001 (2023)

Many body localization transition with correlated disorder

Authors: Zhengyan Darius Shi, Vedika Khemani, Romain Vasseur, Sarang Gopalakrishnan

Abstract: We address the critical properties of the many-body localization (MBL) phase transition in one-dimensional systems subject to spatially correlated disorder. We consider a general family of disorder models, parameterized by how strong the fluctuations of the disordered couplings are when coarse-grained over a region of size $\ell$. For uncorrelated randomness, the characteristic scale for these flu… ▽ More We address the critical properties of the many-body localization (MBL) phase transition in one-dimensional systems subject to spatially correlated disorder. We consider a general family of disorder models, parameterized by how strong the fluctuations of the disordered couplings are when coarse-grained over a region of size $\ell$. For uncorrelated randomness, the characteristic scale for these fluctuations is $\sqrt{\ell}$; more generally they scale as $\ell^γ$. We discuss both positively correlated disorder ($1/2 < γ< 1$) and anticorrelated, or "hyperuniform," disorder ($γ< 1/2$). We argue that anticorrelations in the disorder are generally irrelevant at the MBL transition. Moreover, assuming the MBL transition is described by the recently developed renormalization-group scheme of Morningstar \emph{et al.} [Phys. Rev. B 102, 125134, (2020)], we argue that even positively correlated disorder leaves the critical theory unchanged, although it modifies certain properties of the many-body localized phase. △ Less

Submitted 6 May, 2022; v1 submitted 12 April, 2022; originally announced April 2022.

Comments: 25 pages, including 9 figures, 1 table, and 3 appendices (additional reference added in v2)

Journal ref: Phys. Rev. B 106, 144201 (2022)

Distinct universality classes of diffusive transport from full counting statistics

Authors: Sarang Gopalakrishnan, Alan Morningstar, Romain Vasseur, Vedika Khemani

Abstract: The hydrodynamic transport of local conserved densities furnishes an effective coarse-grained description of the dynamics of a many-body quantum system. However, the full quantum dynamics contains much more structure beyond the simplified hydrodynamic description. Here we show that systems with the same hydrodynamics can nevertheless belong to distinct dynamical universality classes, as revealed b… ▽ More The hydrodynamic transport of local conserved densities furnishes an effective coarse-grained description of the dynamics of a many-body quantum system. However, the full quantum dynamics contains much more structure beyond the simplified hydrodynamic description. Here we show that systems with the same hydrodynamics can nevertheless belong to distinct dynamical universality classes, as revealed by new classes of experimental observables accessible in synthetic quantum systems, which can, for instance, measure simultaneous site-resolved snapshots of all of the particles in a system. Specifically, we study the full counting statistics of spin transport, whose first moment is related to linear-response transport, but the higher moments go beyond. We present an analytic theory of the full counting statistics of spin transport in various integrable and non-integrable anisotropic one-dimensional spin models, including the XXZ spin chain. We find that spin transport, while diffusive on average, is governed by a distinct non-Gaussian dynamical universality class in the models considered. We consider a setup in which the left and right half of the chain are initially created at different magnetization densities, and consider the probability distribution of the magnetization transferred between the two half-chains. We derive a closed-form expression for the probability distribution of the magnetization transfer, in terms of random walks on the half-line. We show that this distribution strongly violates the large-deviation form expected for diffusive chaotic systems, and explain the physical origin of this violation. We discuss the crossovers that occur as the initial state is brought closer to global equilibrium. Our predictions can directly be tested in experiments using quantum gas microscopes or superconducting qubit arrays. △ Less

Submitted 13 April, 2023; v1 submitted 17 March, 2022; originally announced March 2022.

Comments: 11pp., 7 figures

Journal ref: Physical Review B 109, 024417 (2024)

Integrability breaking in the Rule 54 cellular automaton

Authors: Javier Lopez-Piqueres, Sarang Gopalakrishnan, Romain Vasseur

Abstract: Cellular automata have recently attracted a lot of attention as testbeds to explore the emergence of many-body quantum chaos and hydrodynamics. We consider the Rule 54 model, one of the simplest interacting integrable models featuring two species of quasiparticles (solitons), in the presence of an integrability-breaking perturbation that allows solitons to backscatter. We study the onset of therma… ▽ More Cellular automata have recently attracted a lot of attention as testbeds to explore the emergence of many-body quantum chaos and hydrodynamics. We consider the Rule 54 model, one of the simplest interacting integrable models featuring two species of quasiparticles (solitons), in the presence of an integrability-breaking perturbation that allows solitons to backscatter. We study the onset of thermalization and diffusive hydrodynamics in this model, compute perturbatively the diffusion constant of tracer particles, and comment on its relation to transport coefficients. △ Less

Submitted 10 April, 2022; v1 submitted 10 March, 2022; originally announced March 2022.

Comments: v2. Corrected notation inconsistencies, added a reference. v1. To appear in special issue "Hydrodynamics of Low-Dimensional Quantum Systems" of J. Phys. A

Journal ref: J. Phys. A: Math. Theor. 55 234005 (2022)

Field theory of charge sharpening in symmetric monitored quantum circuits

Authors: Fergus Barratt, Utkarsh Agrawal, Sarang Gopalakrishnan, David A. Huse, Romain Vasseur, Andrew C. Potter

Abstract: Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of cha… ▽ More Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to slowly decaying spatial fluctuations of charge in the steady state, and a charge-sharp phase in which measurements collapse quantum fluctuations of charge without destroying the volume-law entanglement of neutral degrees of freedom. By taking a continuous-time, weak-measurement limit, we construct a controlled replica field theory description of these phases and their intervening charge-sharpening transition in one spatial dimension. We find that the charge fuzzy phase is a critical phase with continuously evolving critical exponents that terminates in a modified Kosterlitz-Thouless transition to the short-range correlated charge-sharp phase. We numerically corroborate these scaling predictions also hold for discrete-time projective-measurement circuit models using large-scale matrix-product state simulations, and discuss generalizations to higher dimensions. △ Less

Submitted 17 November, 2021; originally announced November 2021.

Comments: 5+8 pages, 3 figures

Journal ref: Phys. Rev. Lett. 129, 120604 (2022)

Entanglement dynamics in hybrid quantum circuits

Authors: Andrew C. Potter, Romain Vasseur

Abstract: The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple universal "laws". This same philosophy promises powerful methods for studying the dynamics of quantum information in ideal and noisy quantum circuits -- for whic… ▽ More The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple universal "laws". This same philosophy promises powerful methods for studying the dynamics of quantum information in ideal and noisy quantum circuits -- for which classical description of individual circuits is expected to be generically intractable. Here, we review recent progress in understanding the dynamics of quantum information in ensembles of random quantum circuits, through a stat-mech lens. We begin by reviewing discoveries of universal features of entanglement growth, operator spreading, thermalization, and chaos in unitary random quantum circuits, and their relation to stat-mech problems of random surface growth and noisy hydrodynamics. We then explore the dynamics of monitored random circuits, which can loosely be thought of as noisy dynamics arising from an environment monitoring the system, and exhibit new types of measurement-induced phases and criticality. Throughout, we attempt to give a pedagogical introduction to various technical methods, and to highlight emerging connections between concepts in stat-mech, quantum information and quantum communication theory. △ Less

Submitted 23 November, 2021; v1 submitted 15 November, 2021; originally announced November 2021.

Comments: v2: various updated sections, new figures. Chapter in "Springer volume: Entanglement in Spin Chains -- Theory and Quantum Technology Applications"

Journal ref: Chapter in "Entanglement in Spin Chains. Quantum Science and Technology", Springer, pages 211-249 (2022)

Statistical mechanics model for Clifford random tensor networks and monitored quantum circuits

Authors: Yaodong Li, Romain Vasseur, Matthew P. A. Fisher, Andreas W. W. Ludwig

Abstract: We introduce an exact mapping of Clifford (stabilizer) random tensor networks (RTNs) and monitored quantum circuits, onto a statistical mechanics model. With Haar unitaries, the fundamental degrees of freedom ('spins') are permutations because all operators commuting with the action of the unitaries on a tensor product arise from permutations of the tensor factors ('Schur-Weyl duality'). For unita… ▽ More We introduce an exact mapping of Clifford (stabilizer) random tensor networks (RTNs) and monitored quantum circuits, onto a statistical mechanics model. With Haar unitaries, the fundamental degrees of freedom ('spins') are permutations because all operators commuting with the action of the unitaries on a tensor product arise from permutations of the tensor factors ('Schur-Weyl duality'). For unitaries restricted to the smaller Clifford group, the set of commuting operators, the 'commutant', forming the new 'spin' degrees of freedom, will be larger. We use the recent full characterization of this commutant by Gross et al., Comm. Math. Phys. 385, 1325 (2021), to construct the Clifford statistical mechanics models for on-site Hilbert space dimensions which are powers of a prime number $p$. We show that the Boltzmann weights are invariant under a symmetry group involving orthogonal matrices with entries in the finite number field ${\bf F}_p$. This implies that the symmetry group, and consequently all universal properties of entanglement transitions in Clifford circuits and RTNs will in general depend on, and only on the prime $p$. We show that Clifford monitored circuits with on-site Hilbert space dimension $d=p^M$ are described by percolation in the limits $d \to \infty$ at (a) $p=$ fixed but $M\to \infty$, and at (b) $M= 1$ but $p \to \infty$. In the limit (a) we calculate the effective central charge, and in the limit (b) we derive the following universal minimal cut entanglement entropy $S_A =(\sqrt{3}/π)\ln p \ln L_A$ for $d=p$ large at the transition. We verify those predictions numerically, and present extensive numerical results for critical exponents at the transition in monitored Clifford circuits for prime number on-site Hilbert space dimension $d=p$ for a variety of different values of $p$, and find that they approach percolation values at large $p$. △ Less

Submitted 16 April, 2025; v1 submitted 6 October, 2021; originally announced October 2021.

Comments: 23 pages, 5 figures. Abstract shortened to meet arxiv requirements, see pdf for full abstract. v2: Discussion on multifractality in Clifford circuits added. Published version

Journal ref: Phys. Rev. B 109, 174307 (2024)

Subdiffusion and many-body quantum chaos with kinetic constraints

Authors: Hansveer Singh, Brayden Ware, Romain Vasseur, Aaron J. Friedman

Abstract: We investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints. Using random unitary circuits, we compute ensemble-averaged spectral form factors and linear-response correlation functions, and find that their characteristic time scales are given by the inverse gap of an effective Hamiltonian$-$or equivalently, a transfer matrix desc… ▽ More We investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints. Using random unitary circuits, we compute ensemble-averaged spectral form factors and linear-response correlation functions, and find that their characteristic time scales are given by the inverse gap of an effective Hamiltonian$-$or equivalently, a transfer matrix describing a classical Markov process. Our approach allows us to connect directly the Thouless time, $t_{\text{Th}}$, determined by the spectral form factor, to transport properties and linear response correlators. Using tensor network methods, we determine the dynamical exponent, $z$, for a number of constrained, conserving models. We find universality classes with diffusive, subdiffusive, quasilocalized, and localized dynamics, depending on the severity of the constraints. In particular, we show that quantum systems with 'Fredkin constraints' exhibit anomalous transport with dynamical exponent $z \simeq 8/3$. △ Less

Submitted 2 December, 2021; v1 submitted 4 August, 2021; originally announced August 2021.

Comments: 4 pages, 2 figures plus 26 pages supplemental material, v2: additional results, new XNOR constraint

Journal ref: Phys. Rev. Lett. 127, 230602 (2021)

Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits

Authors: Utkarsh Agrawal, Aidan Zabalo, Kun Chen, Justin H. Wilson, Andrew C. Potter, J. H. Pixley, Sarang Gopalakrishnan, Romain Vasseur

Abstract: Monitored quantum circuits can exhibit an entanglement transition as a function of the rate of measurements, stemming from the competition between scrambling unitary dynamics and disentangling projective measurements. We study how entanglement dynamics in non-unitary quantum circuits can be enriched in the presence of charge conservation, using a combination of exact numerics and a mapping onto a… ▽ More Monitored quantum circuits can exhibit an entanglement transition as a function of the rate of measurements, stemming from the competition between scrambling unitary dynamics and disentangling projective measurements. We study how entanglement dynamics in non-unitary quantum circuits can be enriched in the presence of charge conservation, using a combination of exact numerics and a mapping onto a statistical mechanics model of constrained hard-core random walkers. We uncover a charge-sharpening transition that separates different scrambling phases with volume-law scaling of entanglement, distinguished by whether measurements can efficiently reveal the total charge of the system. We find that while Rényi entropies grow sub-ballistically as $\sqrt{t}$ in the absence of measurement, for even an infinitesimal rate of measurements, all average Rényi entropies grow ballistically with time $\sim t$. We study numerically the critical behavior of the charge-sharpening and entanglement transitions in U(1) circuits, and show that they exhibit emergent Lorentz invariance and can also be diagnosed using scalable local ancilla probes. Our statistical mechanical mapping technique readily generalizes to arbitrary Abelian groups, and offers a general framework for studying dissipatively-stabilized symmetry-breaking and topological orders. △ Less

Submitted 4 October, 2022; v1 submitted 21 July, 2021; originally announced July 2021.

Comments: Updated some statements and a figure. 29 pages, 17 figures

Journal ref: Phys. Rev. X 12, 041002 2022

Realizing a dynamical topological phase in a trapped-ion quantum simulator

Authors: Philipp T. Dumitrescu, Justin Bohnet, John Gaebler, Aaron Hankin, David Hayes, Ajesh Kumar, Brian Neyenhuis, Romain Vasseur, Andrew C. Potter

Abstract: Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in (approximately) isolated systems. Here, achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work suggests that these capabilities can enable dynamical phases an… ▽ More Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in (approximately) isolated systems. Here, achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work suggests that these capabilities can enable dynamical phases and critical phenomena that exhibit topologically-robust methods to create, protect, and manipulate quantum entanglement that self-correct against large classes of errors. However, to date, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders. In this work, we demonstrate an emergent dynamical symmetry protected topological phase (EDSPT), in a quasiperiodically-driven array of ten $^{171}\text{Yb}^+$ hyperfine qubits in Honeywell's System Model H1 trapped-ion quantum processor. This phase exhibits edge qubits that are dynamically protected from control errors, cross-talk, and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. This property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit-array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders that would enable error-resilient techniques to manipulate quantum information. △ Less

Submitted 20 July, 2021; originally announced July 2021.

Comments: 6+12 pages; 3+7 figures

Journal ref: Nature 607, 463-467 (2022)

Entanglement transitions from restricted Boltzmann machines

Authors: Raimel Medina, Romain Vasseur, Maksym Serbyn

Abstract: The search for novel entangled phases of matter has lead to the recent discovery of a new class of ``entanglement transitions'', exemplified by random tensor networks and monitored quantum circuits. Most known examples can be understood as some classical ordering transitions in an underlying statistical mechanics model, where entanglement maps onto the free energy cost of inserting a domain wall.… ▽ More The search for novel entangled phases of matter has lead to the recent discovery of a new class of ``entanglement transitions'', exemplified by random tensor networks and monitored quantum circuits. Most known examples can be understood as some classical ordering transitions in an underlying statistical mechanics model, where entanglement maps onto the free energy cost of inserting a domain wall. In this paper, we study the possibility of entanglement transitions driven by physics beyond such statistical mechanics mappings. Motivated by recent applications of neural network-inspired variational Ansätze, we investigate under what conditions on the variational parameters these Ansätze can capture an entanglement transition. We study the entanglement scaling of short-range restricted Boltzmann machine (RBM) quantum states with random phases. For uncorrelated random phases, we analytically demonstrate the absence of an entanglement transition and reveal subtle finite size effects in finite size numerical simulations. Introducing phases with correlations decaying as $1/r^α$ in real space, we observe three regions with a different scaling of entanglement entropy depending on the exponent $α$. We study the nature of the transition between these regions, finding numerical evidence for critical behavior. Our work establishes the presence of long-range correlated phases in RBM-based wave functions as a required ingredient for entanglement transitions. △ Less

Submitted 12 July, 2021; originally announced July 2021.

Comments: 10 pages, 4 figures

Journal ref: Phys. Rev. B 104, 104205 (2021)

Operator scaling dimensions and multifractality at measurement-induced transitions

Authors: Aidan Zabalo, Michael J. Gullans, Justin H. Wilson, Romain Vasseur, Andreas W. W. Ludwig, Sarang Gopalakrishnan, David A. Huse, J. H. Pixley

Abstract: Repeated local measurements of quantum many body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases yield quantitatively similar values of the critical exponents, making it unclear if there is only one underlying universality class. Here, we directly probe the pro… ▽ More Repeated local measurements of quantum many body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases yield quantitatively similar values of the critical exponents, making it unclear if there is only one underlying universality class. Here, we directly probe the properties of the conformal field theories governing these MIPTs using a numerical transfer-matrix method, which allows us to extract the effective central charge, as well as the first few low-lying scaling dimensions of operators at these critical points. Our results provide convincing evidence that the generic and Clifford MIPTs for qubits lie in different universality classes and that both are distinct from the percolation transition for qudits in the limit of large onsite Hilbert space dimension. For the generic case, we find strong evidence of multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions. △ Less

Submitted 11 February, 2022; v1 submitted 7 July, 2021; originally announced July 2021.

Comments: (6 + 12) pages, (2 + 12) figures, (1 + 2) tables (Updated with published version)

Journal ref: Phys. Rev. Lett. 128, 050602 (2022)

Operator front broadening in chaotic and integrable quantum chains

Authors: Javier Lopez-Piqueres, Brayden Ware, Sarang Gopalakrishnan, Romain Vasseur

Abstract: Operator spreading under unitary time evolution has attracted a lot of attention recently, as a way to probe many-body quantum chaos. While quantities such as out-of-time-ordered correlators (OTOC) do distinguish interacting from non-interacting systems, it has remained unclear to what extent they can truly diagnose chaotic {\it vs} integrable dynamics in many-body quantum systems. Here, we analyz… ▽ More Operator spreading under unitary time evolution has attracted a lot of attention recently, as a way to probe many-body quantum chaos. While quantities such as out-of-time-ordered correlators (OTOC) do distinguish interacting from non-interacting systems, it has remained unclear to what extent they can truly diagnose chaotic {\it vs} integrable dynamics in many-body quantum systems. Here, we analyze operator spreading in generic 1D many-body quantum systems using a combination of matrix product operator (MPO) and analytical techniques, focusing on the operator {\em right-weight}. First, we show that while small bond dimension MPOs allow one to capture the exponentially-decaying tail of the operator front, in agreement with earlier results, they lead to significant quantitative and qualitative errors for the actual front -- defined by the maximum of the right-weight. We find that while the operator front broadens diffusively in both integrable and chaotic interacting spin chains, the precise shape and scaling of the height of the front in integrable systems is anomalous for all accessible times. We interpret these results using a quasiparticle picture. This provides a sharp, though rather subtle signature of many-body quantum chaos in the operator front. △ Less

Submitted 15 September, 2021; v1 submitted 24 March, 2021; originally announced March 2021.

Comments: 9 pages, 9 figure. v2: added references, corrected typos, added Fig 10 in Appendix

Journal ref: Phys. Rev. B 104, 104307 (2021)

Local integrals of motion and the quasiperiodic many-body localization transition

Authors: Hansveer Singh, Brayden Ware, Romain Vasseur, Sarang Gopalakrishnan

Abstract: We study the many body localization (MBL) transition for interacting fermions subject to quasiperiodic potentials by constructing the local integrals of motion (LIOMs) in the MBL phase as time-averaged local operators. We study numerically how these time-averaged operators evolve across the MBL transition. We find that the norm of such time-averaged operators drops discontinuously to zero across t… ▽ More We study the many body localization (MBL) transition for interacting fermions subject to quasiperiodic potentials by constructing the local integrals of motion (LIOMs) in the MBL phase as time-averaged local operators. We study numerically how these time-averaged operators evolve across the MBL transition. We find that the norm of such time-averaged operators drops discontinuously to zero across the transition; as we discuss, this implies that LIOMs abruptly become unstable at some critical localization length of order unity. We analyze the LIOMs using hydrodynamic projections and isolating the part of the operator that is associated with interactions. Equipped with this data we perform a finite-size scaling analysis of the quasiperiodic MBL transition. Our results suggest that the quasiperiodic MBL transition occurs at considerably stronger quasiperiodic modulations, and has a larger correlation-length critical exponent, than previous studies had found. △ Less

Submitted 11 January, 2021; originally announced January 2021.

Comments: 4.5 pages, 1 figure plus 11.5 pages supplemental material

Journal ref: Phys. Rev. B 103, 220201 (2021)

Topological edge modes without symmetry in quasiperiodically driven spin chains

Authors: Aaron J. Friedman, Brayden Ware, Romain Vasseur, Andrew C. Potter

Abstract: We construct an example of a 1$d$ quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. Unlike analogous behavior in static and periodically driven (Floquet) spin chains, this model does not rely upon microscopic symmetry protection: Instead, the edge states are protected purely by emergen… ▽ More We construct an example of a 1$d$ quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. Unlike analogous behavior in static and periodically driven (Floquet) spin chains, this model does not rely upon microscopic symmetry protection: Instead, the edge states are protected purely by emergent dynamical symmetries. We explore the dynamical signatures of this Emergent Dynamical Symmetry-Protected Topological (EDSPT) order through exact numerics, time evolving block decimation, and analytic high-frequency expansion, finding evidence that the EDSPT is a stable dynamical phase protected by bulk many-body localization up to (at least) stretched-exponentially long time scales, and possibly beyond. We argue that EDSPTs are special to the quasiperiodically driven setting, and cannot arise in Floquet systems. Moreover, we find evidence of a new type of boundary criticality, in which the edge spin dynamics transition from quasiperiodic to chaotic, leading to bulk thermalization. △ Less

Submitted 7 September, 2020; originally announced September 2020.

Comments: 7+8 pages, 5 figures

Journal ref: Phys. Rev. B 105, 115117 (2022)

Topological and symmetry-enriched random quantum critical points

Authors: Carlos M. Duque, Hong-Ye Hu, Yi-Zhuang You, Vedika Khemani, Ruben Verresen, Romain Vasseur

Abstract: We study how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. These are the disordered analogues of gapless topological phases. Using real-space and density matrix renormalization group approaches, we analyze the boundary and bulk critical behavior of such symmetry-enriched random quantum… ▽ More We study how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. These are the disordered analogues of gapless topological phases. Using real-space and density matrix renormalization group approaches, we analyze the boundary and bulk critical behavior of such symmetry-enriched random quantum spin chains. We uncover a new class of symmetry-enriched infinite randomness fixed points: while local bulk properties are indistinguishable from conventional random singlet phases, nonlocal observables and boundary critical behavior are controlled by a different renormalization group fixed point. We also illustrate how such new quantum critical points emerge naturally in Floquet systems. △ Less

Submitted 18 December, 2020; v1 submitted 5 August, 2020; originally announced August 2020.

Comments: 4+epsilon pages+supp mat, 2 figures. v2: New discussion of Floquet systems. A new co-author has been added

Journal ref: Phys. Rev. B 103, 100207 (2021)