Showing 1–50 of 137 results for author: Cohen, G

Application of the exact-factorization density-functional perturbation approach to pentacene crystal and monolayer MoS2

Authors: Rachel Steinitz-Eliyahu, Galit Cohen, Guy Vosco, E. K. U. Gross, Ryan Requist, Sivan Refaely-Abramson

Abstract: Non-adiabatic effects arising from electron-phonon interactions are often neglected within the Born-Oppenheimer (BO) approximation, which assumes that electronic states adjust instantaneously to nuclear motion. The exact factorization (EF) formalism provides a rigorous framework for treating such effects beyond the adiabatic regime and has recently been adapted to density functional theory (DFT) i… ▽ More Non-adiabatic effects arising from electron-phonon interactions are often neglected within the Born-Oppenheimer (BO) approximation, which assumes that electronic states adjust instantaneously to nuclear motion. The exact factorization (EF) formalism provides a rigorous framework for treating such effects beyond the adiabatic regime and has recently been adapted to density functional theory (DFT) in the harmonic limit. Building on these foundations, we previously introduced an EF-based perturbative scheme, the EF density-functional perturbation theory (EF-DFPT), that enables the computation of phonon-driven non-adiabatic (NA) corrections to Kohn-Sham (KS) electronic states, up to second order in nuclear displacements. Here, we present the first implementation and application of EF-DFPT to extended periodic materials, focusing on its impact on experimentally relevant observables. Using the pentacene molecular crystal and monolayer MoS2 as representative soft- and stiff-mode systems, respectively, we demonstrate how NA electron-phonon interactions modify the static dielectric response. We show that these modifications originate from the combined effect of NA phonon-dressed electronic wavefunctions and second-order NA energy renormalizations. The resulting behavior is strongly material dependent: NA effects are negligible in monolayer MoS2, whereas in pentacene they lead to pronounced long-range screening effects associated with soft vibrational modes and enhanced electron-phonon coupling. △ Less

Submitted 11 May, 2026; originally announced May 2026.

Validity and Limits of Low Order Hybridization Expansion Approaches for Multi-Orbital Systems

Authors: Dolev Goldberger, Ido Zemach, Lei Zhang, Yang Yu, Emanuel Gull, Guy Cohen, André Erpenbeck

Abstract: Low-order hybridization expansion methods such as the non-crossing approximation (NCA) and the one-crossing approximation (OCA) are widely used impurity solvers in the study of strongly correlated systems, yet their accuracy in genuine multi-orbital settings remains poorly understood. Using the decoupled orbital limit as a controlled reference point, we derive analytic results connecting multi-orb… ▽ More Low-order hybridization expansion methods such as the non-crossing approximation (NCA) and the one-crossing approximation (OCA) are widely used impurity solvers in the study of strongly correlated systems, yet their accuracy in genuine multi-orbital settings remains poorly understood. Using the decoupled orbital limit as a controlled reference point, we derive analytic results connecting multi-orbital restricted propagators and Green's functions to their single-orbital counterparts, identify the diagrammatic mechanisms responsible for the breakdown of low-order methods in multi-orbital settings, and determine their regimes of applicability. Our central finding is that the accuracy of these methods is governed by the least correlated orbital: i.e., the orbital with the most rapidly decaying retarded Green's function. That orbital's properties are transferred to all other orbitals through a spurious coupling generated by the truncated expansion, thereby suppressing correlation-induced features such as the Kondo resonance. This occurs even in orbitals that are themselves strongly correlated within single-orbital calculations using the same approximation scheme. We confirm this numerically across representative two-orbital model systems in the steady-state, systematically identifying the parameter regimes in which low-order methods succeed or fail. Our results provide a practical guide for assessing when insights from single-orbital calculations carry over to multi-orbital settings, and serve as a benchmark for the development and validation of higher-order multi-orbital impurity solvers. △ Less

Submitted 4 May, 2026; originally announced May 2026.

Transient Dynamical Phase Diagram of the Spin-Boson Model at Finite Temperature

Authors: Olga Goulko, Hsing-Ta Chen, Moshe Goldstein, Guy Cohen

Abstract: We present numerically exact inchworm quantum Monte Carlo results for the real-time dynamics of the spin polarization in the sub-Ohmic spin-boson model at finite temperature. We focus in particular on the localization and coherence behavior of the model, extending our previous study at low temperature [Phys. Rev. Lett. 134, 056502 (2025)]. As the temperature increases, the system becomes less loca… ▽ More We present numerically exact inchworm quantum Monte Carlo results for the real-time dynamics of the spin polarization in the sub-Ohmic spin-boson model at finite temperature. We focus in particular on the localization and coherence behavior of the model, extending our previous study at low temperature [Phys. Rev. Lett. 134, 056502 (2025)]. As the temperature increases, the system becomes less localized and less coherent. The loss of coherence, which is controlled by two independent mechanisms -- a smooth damping-driven crossover and a sharp frequency-driven transition -- exhibits a nontrivial temperature dependence. While both types of coherence loss occur at lower coupling in the high temperature regime, the frequency exhibits a sharper drop at high temperatures and this drop is observed for all values of the sub-Ohmic exponent, in contrast to the zero-temperature case. We discuss the full temperature-dependent dynamical phase diagram of the system and the interplay between coherence and localization across a wide range of physical parameters. △ Less

Submitted 30 March, 2026; v1 submitted 2 September, 2025; originally announced September 2025.

Journal ref: Phys. Rev. B 113, 115155 (2026)

Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm

Authors: Andre Erpenbeck, Yuanran Zhu, Yang Yu, Lei Zhang, Richard Gerum, Olga Goulko, Chao Yang, Guy Cohen, Emanuel Gull

Abstract: Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In th… ▽ More Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical data from simulations of quantum systems. We evaluate ESPRIT's performance in the presence of noise and compare it to other extrapolation methods. We demonstrate its ability to extract information from short-time dynamics to reliably predict long-time behavior and determine the minimum time interval required for accurate results. We discuss how this insight can be leveraged in numerical methods that propagate quantum systems in time, and show how ESPRIT can predict infinite-time values of dynamical observables, offering a purely data-driven approach to characterizing quantum phases. △ Less

Submitted 25 March, 2026; v1 submitted 16 June, 2025; originally announced June 2025.

Journal ref: Phys. Rev. B 113, 115129 (2026)

Inchworm tensor train hybridization expansion quantum impurity solver

Authors: Yang Yu, André Erpenbeck, Dominika Zgid, Guy Cohen, Olivier Parcollet, Emanuel Gull

Abstract: The investigation of quantum impurity models plays a crucial role in condensed matter physics because of their wide-ranging applications, such as embedding theories and transport problems. Traditional methods often fall short of producing accurate results for multi-orbital systems with complex interactions and off-diagonal hybridizations. Recently, tensor-train-based integration and summation tech… ▽ More The investigation of quantum impurity models plays a crucial role in condensed matter physics because of their wide-ranging applications, such as embedding theories and transport problems. Traditional methods often fall short of producing accurate results for multi-orbital systems with complex interactions and off-diagonal hybridizations. Recently, tensor-train-based integration and summation techniques have shown promise as effective alternatives. In this study, we use tensor train methods to tackle quantum impurity problems formulated within the imaginary-time inchworm hybridization expansion framework. We identify key challenges in the inchworm expansion itself and its interplay with tensor-train-based methods. We demonstrate the accuracy and versatility of our approach by solving general quantum impurity problems. Our results suggest that tensor-train decomposition schemes offer a viable path toward accurate and efficient multi-orbital impurity solvers. △ Less

Submitted 12 August, 2025; v1 submitted 21 May, 2025; originally announced May 2025.

Comments: 20 pages, 9 figures

Journal ref: Phys. Rev. B 112, 085120 (2025)

Non-adiabaticity from first principles: the exact-factorization approach for solids

Authors: Galit Cohen, Rachel Steinitz-Eliyahu, E. K. U. Gross, Sivan Refaely-Abramson, Ryan Requist

Abstract: The thorough treatment of electron-lattice interactions from first principles is one of the main goals in condensed matter physics. While the commonly applied adiabatic Born-Oppenheimer approximation is sufficient for describing many physical phenomena, it is limited in its ability to capture meaningful features originating from non-adiabatic coupling effects. The exact factorization method, start… ▽ More The thorough treatment of electron-lattice interactions from first principles is one of the main goals in condensed matter physics. While the commonly applied adiabatic Born-Oppenheimer approximation is sufficient for describing many physical phenomena, it is limited in its ability to capture meaningful features originating from non-adiabatic coupling effects. The exact factorization method, starting from the full Hamiltonian of electrons and nuclei, provides a way to systematically account for non-adiabatic effects. This formalism was recently developed into an ab initio density functional theory framework. Within this framework we here develop a perturbative approach to the electronic states in solid state materials. We derive exact-factorization-based perturbations of the Kohn-Sham states up to second order in the nuclear displacements. These non-adiabatic features in the calculated energy and wavefunction corrections are expressed in terms of readily available density functional perturbation theory components. △ Less

Submitted 11 February, 2025; originally announced February 2025.

Defect Positioning in Combinatorial Metamaterials

Authors: Chaviva Sirote-Katz, Yotam M. Y. Feldman, Guy Cohen, Tamás Kálmán, Yair Shokef

Abstract: Combinatorial mechanical metamaterials are made of anisotropic, flexible blocks, such that multiple metamaterials may be constructed using a single block type, and the system's response depends on the frustration (or its absence) due to the mutual orientations of the blocks within the lattice. Specifically, any minimal loop of blocks that may not simultaneously deform in their softest mode defines… ▽ More Combinatorial mechanical metamaterials are made of anisotropic, flexible blocks, such that multiple metamaterials may be constructed using a single block type, and the system's response depends on the frustration (or its absence) due to the mutual orientations of the blocks within the lattice. Specifically, any minimal loop of blocks that may not simultaneously deform in their softest mode defines a mechanical defect at the vertex (in two dimensions) or edge (in three dimensions) that the loop encircles. Defects stiffen the metamaterial, and allow to design the spatial patterns of stress and deformation as the system is externally loaded. We study the ability to place defects at arbitrary positions in metamaterials made of a family of block types that we recently introduced for the square, honeycomb, and cubic lattices. Alongside blocks for which we show that any defect configuration is possible, we identify situations in which not all sets are realizable as defects. One of the restrictions is that in three dimensions, defected edges form closed curves. Even in cases when not all geometries of defect lines are possible, we show how to produce defect lines of arbitrary knottedness. △ Less

Submitted 9 June, 2025; v1 submitted 2 December, 2024; originally announced December 2024.

Comments: See accompanying paper: Breaking Mechanical Holography in Combinatorial Metamaterials arXiv:2411.15760

Journal ref: Physical Review Research 7, 033005 (2025)

Nonequilibrium Steady State Full Counting Statistics in the Noncrossing Approximation

Authors: Ido Zemach, Andre Erpenbeck, Emanuel Gull, Guy Cohen

Abstract: Quantum transport is often characterized not just by mean observables like the particle or energy current, but by their fluctuations and higher moments, which can act as detailed probes of the physical mechanisms at play. However, relatively few theoretical methods are able to access the full counting statistics (FCS) of transport processes through electronic junctions in strongly correlated regim… ▽ More Quantum transport is often characterized not just by mean observables like the particle or energy current, but by their fluctuations and higher moments, which can act as detailed probes of the physical mechanisms at play. However, relatively few theoretical methods are able to access the full counting statistics (FCS) of transport processes through electronic junctions in strongly correlated regimes. While most experiments are concerned with the steady state properties, most accurate theoretical methods rely on computationally expensive propagation from a tractable initial state. Here, we propose a simple approach for computing the FCS through a junction directly at the steady state, utilizing the propagator noncrossing approximation (NCA). Compared to time propagation, our method offers reduced computational cost at the same level of approximation; but the idea can also be used within other approximations or as a basis for numerically exact techniques. We demonstrate the method's capabilities by investigating the impact of lead dimensionality on electronic transport in the nonequilibrium Anderson impurity model at the onset of Kondo physics. Our results reveal a distinct signature of one dimensional leads in the noise and Fano factor not present for other dimensionalities, showing the potential of FCS measurements as a probe of the environment surrounding a quantum dot. △ Less

Submitted 18 August, 2024; originally announced August 2024.

Steady-state properties of multi-orbital systems using quantum Monte Carlo

Authors: Andre Erpenbeck, Thomas Blommel, Lei Zhang, Wei-Ting Lin, Guy Cohen, Emanuel Gull

Abstract: A precise dynamical characterization of quantum impurity models with multiple interacting orbitals is challenging. In quantum Monte Carlo methods, this is embodied by sign problems. A dynamical sign problem makes it exponentially difficult to simulate long times. A multi-orbital sign problem generally results in a prohibitive computational cost for systems with multiple impurity degrees of freedom… ▽ More A precise dynamical characterization of quantum impurity models with multiple interacting orbitals is challenging. In quantum Monte Carlo methods, this is embodied by sign problems. A dynamical sign problem makes it exponentially difficult to simulate long times. A multi-orbital sign problem generally results in a prohibitive computational cost for systems with multiple impurity degrees of freedom even in static equilibrium calculations. Here, we present a numerically exact inchworm method that simultaneously alleviates both sign problems, enabling simulation of multi-orbital systems directly in the equilibrium or nonequilibrium steady-state. The method combines ideas from the recently developed steady-state inchworm Monte Carlo framework [Phys. Rev. Lett. 130, 186301 (2023)] with other ideas from the equilibrium multi-orbital inchworm algorithm [Phys. Rev. Lett. 124, 206405 (2020)]. We verify our method by comparison with analytical limits and numerical results from previous methods. △ Less

Submitted 30 June, 2024; originally announced July 2024.

Nonequilibrium entropy from density estimation

Authors: Samuel D. Gelman, Guy Cohen

Abstract: Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated configurations. However, modern machine learning algorithms can estimate the probability density characterizing an ensemble of images, given nothing more than… ▽ More Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated configurations. However, modern machine learning algorithms can estimate the probability density characterizing an ensemble of images, given nothing more than sample images assumed to be drawn from this distribution. We show that by mapping system configurations to images, such approaches can be adapted to the efficient estimation of the density, and therefore the entropy, from simulated or experimental data. We then use this idea to obtain entropic limit cycles in a kinetic Ising model driven by an oscillating magnetic field. Despite being a global probe, we demonstrate that this allows us to identify and characterize stochastic dynamics at parameters near the dynamical phase transition. △ Less

Submitted 8 May, 2024; originally announced May 2024.

Unsupervised learning approach to quantum wavepacket dynamics from coupled temporal-spatial correlations

Authors: Adva Baratz, Galit Cohen, Sivan Refaely-Abramson

Abstract: Understanding complex quantum dynamics in realistic materials requires insight into the underlying correlations dominating the interactions between the participating particles. Due to the wealth of information involved in these processes, applying artificial intelligence methods is compelling. Yet, unsupervised data-driven approaches typically focus on maximal variations of the individual componen… ▽ More Understanding complex quantum dynamics in realistic materials requires insight into the underlying correlations dominating the interactions between the participating particles. Due to the wealth of information involved in these processes, applying artificial intelligence methods is compelling. Yet, unsupervised data-driven approaches typically focus on maximal variations of the individual components, rather than considering the correlations between them. Here we present an approach that recognizes correlation patterns to explore convoluted dynamical processes. Our scheme is using singular value decomposition (SVD) to extract dynamical features, unveiling the internal temporal-spatial interrelations that generate the dynamical mechanisms. We apply our approach to study light-induced wavepacket propagation in organic crystals, of interest for applications in material based quantum computing and quantum information science. We show how transformation from the input momentum and time coordinates onto a new correlation-induced coordinate space allows direct recognition of the relaxation and dephasing components dominating the dynamics and demonstrate their dependence on the initial pulse shape. Entanglement of the dynamical features is suggested as a pathway to reproduce the information required for further explainability of these mechanisms. Our method offers a route for elucidating complex dynamical processes using unsupervised AI-based analysis in multi-component systems. △ Less

Submitted 18 April, 2024; originally announced April 2024.

Transient dynamical phase diagram of the spin-boson model

Authors: Olga Goulko, Hsing-Ta Chen, Moshe Goldstein, Guy Cohen

Abstract: We investigate the real-time dynamics of the sub-Ohmic spin-boson model across a broad range of coupling strengths, using the numerically exact inchworm quantum Monte Carlo algorithm. From short- and intermediate-time dynamics starting from an initially decoupled state, we extract signatures of the zero-temperature quantum phase transition between localized and delocalized states. We show that the… ▽ More We investigate the real-time dynamics of the sub-Ohmic spin-boson model across a broad range of coupling strengths, using the numerically exact inchworm quantum Monte Carlo algorithm. From short- and intermediate-time dynamics starting from an initially decoupled state, we extract signatures of the zero-temperature quantum phase transition between localized and delocalized states. We show that the dynamical phase diagram thus obtained differs from the equilibrium phase diagram in both the values of critical couplings and the associated values of the critical exponent. We also identify and quantitatively analyze two competing mechanisms for the crossover between coherent oscillations and incoherent decay. Deep in the sub-Ohmic regime, the crossover is driven by the damping of the oscillation amplitude, while closer to the Ohmic regime the oscillation frequency itself drops sharply to zero at large coupling. △ Less

Submitted 11 February, 2025; v1 submitted 28 February, 2024; originally announced February 2024.

Journal ref: Phys. Rev. Lett 134, 056502 (2025)

Determinant- and Derivative-Free Quantum Monte Carlo Within the Stochastic Representation of Wavefunctions

Authors: Liam Bernheimer, Hristiana Atanasova, Guy Cohen

Abstract: Describing the ground states of continuous, real-space quantum many-body systems, like atoms and molecules, is a significant computational challenge with applications throughout the physical sciences. Recent progress was made by variational methods based on machine learning (ML) ansatzes. However, since these approaches are based on energy minimization, ansatzes must be twice differentiable. This… ▽ More Describing the ground states of continuous, real-space quantum many-body systems, like atoms and molecules, is a significant computational challenge with applications throughout the physical sciences. Recent progress was made by variational methods based on machine learning (ML) ansatzes. However, since these approaches are based on energy minimization, ansatzes must be twice differentiable. This (a) precludes the use of many powerful classes of ML models; and (b) makes the enforcement of bosonic, fermionic, and other symmetries costly. Furthermore, (c) the optimization procedure is often unstable unless it is done by imaginary time propagation, which is often impractically expensive in modern ML models with many parameters. The stochastic representation of wavefunctions (SRW), introduced in Nat Commun 14, 3601 (2023), is a recent approach to overcoming (c). SRW enables imaginary time propagation at scale, and makes some headway towards the solution of problem (b), but remains limited by problem (a). Here, we argue that combining SRW with path integral techniques leads to a new formulation that overcomes all three problems simultaneously. As a demonstration, we apply the approach to generalized ``Hooke's atoms'': interacting particles in harmonic wells. We benchmark our results against state-of-the-art data where possible, and use it to investigate the crossover between the Fermi liquid and the Wigner molecule within closed-shell systems. Our results shed new light on the competition between interaction-driven symmetry breaking and kinetic-energy-driven delocalization. △ Less

Submitted 13 November, 2024; v1 submitted 9 February, 2024; originally announced February 2024.

Journal ref: Rep. Prog. Phys. 87, 118001 (2024)

Josephson Junction of Nodal Superconductors with Rashba and Ising Spin-Orbit coupling

Authors: Gal Cohen, Ranjani Seshadri, Maxim Khodas, Dganit Meidan

Abstract: We study the effect of a Rashba spin-orbit coupling on the nodal superconducting phase of an Ising superconductor. Such nodal phase was predicted to occur when applying an in-plane field beyond the Pauli limit to a superconducting monolayer transition metal dichalcogenides (TMD). Generically, Rashba spin-orbit is known to lift the chiral symmetry that protects the nodal points, resulting in a full… ▽ More We study the effect of a Rashba spin-orbit coupling on the nodal superconducting phase of an Ising superconductor. Such nodal phase was predicted to occur when applying an in-plane field beyond the Pauli limit to a superconducting monolayer transition metal dichalcogenides (TMD). Generically, Rashba spin-orbit is known to lift the chiral symmetry that protects the nodal points, resulting in a fully gapped phase. However, when the magnetic field is applied along the $Γ-K $ line, a residual vertical mirror symmetry protects a nodal crystalline phase. We study a single-band tight-binding model that captures the low energy physics around the $Γ$ pocket of monolayer TMD. We calculate the topological properties, the edge state structure, and the current phase relation in a Josephson junction geometry of the nodal crystalline phase. We show that while the nodal crystalline phase is characterized by localized edge modes on non-self-reflecting boundaries, the current phase relation exhibits a trivial $2π$ periodicity in the presence of Rashba spin-orbit coupling. △ Less

Submitted 11 January, 2024; originally announced January 2024.

Comments: 9 pages, 9 figures

Dynamical Mean Field Theory of the Bilayer Hubbard Model with Inchworm Monte Carlo

Authors: Dolev Goldberger, Yehonatan Fridman, Emanuel Gull, Eitan Eidelstein, Guy Cohen

Abstract: Dynamical mean-field theory allows access to the physics of strongly correlated materials with nontrivial orbital structure, but relies on the ability to solve auxiliary multi-orbital impurity problems. The most successful approaches to date for solving these impurity problems are the various continuous time quantum Monte Carlo algorithms. Here, we consider perhaps the simplest realization of mult… ▽ More Dynamical mean-field theory allows access to the physics of strongly correlated materials with nontrivial orbital structure, but relies on the ability to solve auxiliary multi-orbital impurity problems. The most successful approaches to date for solving these impurity problems are the various continuous time quantum Monte Carlo algorithms. Here, we consider perhaps the simplest realization of multi-orbital physics: the bilayer Hubbard model on an infinite-coordination Bethe lattice. Despite its simplicity, the majority of this model's phase diagram cannot be predicted by using traditional Monte Carlo methods. We show that these limitations can be largely circumvented by recently introduced Inchworm Monte Carlo techniques. We then explore the model's phase diagram at a variety of interaction strengths, temperatures and filling ratios. △ Less

Submitted 28 November, 2023; originally announced November 2023.

Numerically exact simulation of photo-doped Mott insulators

Authors: Fabian Künzel, André Erpenbeck, Daniel Werner, Enrico Arrigoni, Emanuel Gull, Guy Cohen, Martin Eckstein

Abstract: A description of long-lived photo-doped states in Mott insulators is challenging, as it needs to address exponentially separated timescales. We demonstrate how properties of such states can be computed using numerically exact steady state techniques, in particular Quantum Monte Carlo, by using a time-local ansatz for the distribution function with separate Fermi functions for the electron and hole… ▽ More A description of long-lived photo-doped states in Mott insulators is challenging, as it needs to address exponentially separated timescales. We demonstrate how properties of such states can be computed using numerically exact steady state techniques, in particular Quantum Monte Carlo, by using a time-local ansatz for the distribution function with separate Fermi functions for the electron and hole quasiparticles. The simulations show that the Mott gap remains robust to large photo-doping, and the photo-doped state has hole and electron quasiparticles with strongly renormalized properties. △ Less

Submitted 23 November, 2023; originally announced November 2023.

Comments: 9 pages, 9 figures

Stark-Many body localization in interacting infinite dimensional systems

Authors: Hristiana Atanasova, André Erpenbeck, Emanuel Gull, Yevgeny Bar Lev, Guy Cohen

Abstract: We study bulk particle transport in a Fermi-Hubbard model on an infinite-dimensional Bethe lattice, driven by a constant electric field. Previous numerical studies showed that one dimensional analogs of this system exhibit a breakdown of diffusion due to Stark many-body localization (Stark-MBL) at least up to time which scales exponentially with the system size. Here, we consider systems initially… ▽ More We study bulk particle transport in a Fermi-Hubbard model on an infinite-dimensional Bethe lattice, driven by a constant electric field. Previous numerical studies showed that one dimensional analogs of this system exhibit a breakdown of diffusion due to Stark many-body localization (Stark-MBL) at least up to time which scales exponentially with the system size. Here, we consider systems initially in a spin density wave state using a combination of numerically exact and approximate techniques. We show that for sufficiently weak electric fields, the wave's momentum component decays exponentially with time in a way consistent with normal diffusion. By studying different wavelengths, we extract the dynamical exponent and the generalized diffusion coefficient at each field strength. Interestingly, we find a non-monotonic dependence of the dynamical exponent on the electric field. As the field increases towards a critical value proportional to the Hubbard interaction strength, transport slows down, becoming sub-diffusive. At large interaction strengths, however, transport speeds up again with increasing field, exhibiting super-diffusive characteristics when the electric field is comparable to the interaction strength. Eventually, at the large field limit, localization occurs and the current through the system is suppressed. △ Less

Submitted 15 November, 2023; originally announced November 2023.

Journal ref: Phys. Rev. Lett. 132, 166301 (2024)

Shaping electronic flows with strongly correlated physics

Authors: A. Erpenbeck, E. Gull, G. Cohen

Abstract: Nonequilibrium quantum transport is of central importance in nanotechnology. Its description requires the understanding of strong electronic correlations, which couple atomic-scale phenomena to the nanoscale. So far, research in correlated transport focused predominantly on few-channel transport, precluding the investigation of cross-scale effects. Recent theoretical advances enable the solution o… ▽ More Nonequilibrium quantum transport is of central importance in nanotechnology. Its description requires the understanding of strong electronic correlations, which couple atomic-scale phenomena to the nanoscale. So far, research in correlated transport focused predominantly on few-channel transport, precluding the investigation of cross-scale effects. Recent theoretical advances enable the solution of models that capture the interplay between quantum correlations and confinement beyond a few channels. This problem is the focus of this study. We consider an atomic impurity embedded in a metallic nanosheet spanning two leads, showing that transport is significantly altered by tuning only the phase of a single, local hopping parameter. Furthermore -- depending on this phase -- correlations reshape the electronic flow throughout the sheet, either funneling it through the impurity or scattering it away from a much larger region. This demonstrates the potential for quantum correlations to bridge length scales in the design of nanoelectronic devices and sensors. △ Less

Submitted 15 August, 2023; originally announced August 2023.

The Ferris ferromagnetic resonance technique: principles and applications

Authors: Amit Rothschild, Benjamin Assouline, Nadav Am Shalom, Nirel Bernstein, Goni Daniel, Gil Cohen, Amir Capua

Abstract: Measurements of ferromagnetic resonance (FMR) are pivotal to modern magnetism and spintronics. Recently, we reported on the Ferris FMR technique, which relies on large-amplitude modulation of the externally applied magnetic field. It was shown to benefit from high sensitivity while being broadband. The Ferris FMR also expanded the resonance linewidth such that the sensitivity to spin currents was… ▽ More Measurements of ferromagnetic resonance (FMR) are pivotal to modern magnetism and spintronics. Recently, we reported on the Ferris FMR technique, which relies on large-amplitude modulation of the externally applied magnetic field. It was shown to benefit from high sensitivity while being broadband. The Ferris FMR also expanded the resonance linewidth such that the sensitivity to spin currents was enhanced as well. Eventually, the spin Hall angle (θ_SH) was measurable even in wafer-level measurements that require low current densities to reduce the Joule heating. Despite the various advantages, analysis of the Ferris FMR response is limited to numerical modeling where the linewidth depends on multiple factors such as the field modulation profile and the magnetization saturation. Here, we describe in detail the basic principles of operation of the Ferris FMR and discuss its applicability and engineering considerations. We demonstrated these principles in a measurement of the orbital Hall effect taking place in Cu, using an Au layer as the orbital to spin current converter. This illustrates the potential of the Ferris FMR for the future development of spintronics technology. △ Less

Submitted 31 May, 2023; originally announced June 2023.

Phonon-driven femtosecond dynamics of excitons in crystalline pentacene from first principles

Authors: Galit Cohen, Jonah B. Haber, Jeffrey B. Neaton, Diana Y. Qiu, Sivan Refaely-Abramson

Abstract: Non-radiative exciton relaxation processes are critical for energy transduction efficiencies in optoelectronic materials, but how these processes are connected to the underlying crystal structure and its associated electron, exciton, and phonon band structures is poorly understood. Here, we present a first-principles approach to explore exciton relaxation pathways in pentacene, a paradigmatic mole… ▽ More Non-radiative exciton relaxation processes are critical for energy transduction efficiencies in optoelectronic materials, but how these processes are connected to the underlying crystal structure and its associated electron, exciton, and phonon band structures is poorly understood. Here, we present a first-principles approach to explore exciton relaxation pathways in pentacene, a paradigmatic molecular crystal and optoelectronic semiconductor. We compute the momentum- and band-resolved exciton-phonon interactions, and use them to analyse key scattering channels. We find that exciton intraband transitions on femtosecond timescales leading to dark-state occupation is a dominant nonradiative relaxation channel in pentacene. We further show how the nature of real-time propagation of the exciton wavepacket is connected with the longitudinal-transverse exciton splitting, stemming from crystal anisotropy, and concomitant anisotropic exciton and phonon dispersions. Our results provide a framework for understanding time-resolved exciton propagation and energy transfer in molecular crystals and beyond. △ Less

Submitted 7 May, 2023; originally announced May 2023.

A Tensor Train Continuous Time Solver for Quantum Impurity Models

Authors: A. Erpenbeck, W. -T. Lin, T. Blommel, L. Zhang, S. Iskakov, L. Bernheimer, Y. Núñez-Fernández, G. Cohen, O. Parcollet, X. Waintal, E. Gull

Abstract: The simulation of strongly correlated quantum impurity models is a significant challenge in modern condensed matter physics that has multiple important applications. Thus far, the most successful methods for approaching this challenge involve Monte Carlo techniques that accurately and reliably sample perturbative expansions to any order. However, the cost of obtaining high precision through these… ▽ More The simulation of strongly correlated quantum impurity models is a significant challenge in modern condensed matter physics that has multiple important applications. Thus far, the most successful methods for approaching this challenge involve Monte Carlo techniques that accurately and reliably sample perturbative expansions to any order. However, the cost of obtaining high precision through these methods is high. Recently, tensor train decomposition techniques have been developed as an alternative to Monte Carlo integration. In this study, we apply these techniques to the single-impurity Anderson model at equilibrium by calculating the systematic expansion in power of the hybridization of the impurity with the bath. We demonstrate the performance of the method in a paradigmatic application, examining the first-order phase transition on the infinite dimensional Bethe lattice, which can be mapped to an impurity model through dynamical mean field theory. Our results indicate that using tensor train decomposition schemes allows the calculation of finite-temperature Green's functions and thermodynamic observables with unprecedented accuracy. The methodology holds promise for future applications to frustrated multi-orbital systems, using a combination of partially summed series with other techniques pioneered in diagrammatic and continuous-time quantum Monte Carlo. △ Less

Submitted 20 March, 2023; originally announced March 2023.

Journal ref: Phys. Rev. B 107, 245135 (2023)

Quantum Monte Carlo in the steady-state

Authors: André Erpenbeck, Emanuel Gull, Guy Cohen

Abstract: We present a numerically exact steady-state inchworm Monte Carlo method for nonequilibrium quantum impurity models. Rather than propagating an initial state to long times, the method is directly formulated in the steady-state. This eliminates any need to traverse the transient dynamics and grants access to a much larger range of parameter regimes at vastly reduced computational costs. We benchmark… ▽ More We present a numerically exact steady-state inchworm Monte Carlo method for nonequilibrium quantum impurity models. Rather than propagating an initial state to long times, the method is directly formulated in the steady-state. This eliminates any need to traverse the transient dynamics and grants access to a much larger range of parameter regimes at vastly reduced computational costs. We benchmark the method on equilibrium Green's functions of quantum dots in the noninteracting limit and in the unitary limit of the Kondo regime. We then consider correlated materials described with dynamical mean field theory and driven away from equilibrium by a bias voltage. We show that the response of a correlated material to a bias voltage differs qualitatively from the splitting of the Kondo resonance observed in bias-driven quantum dots. △ Less

Submitted 22 September, 2022; v1 submitted 15 July, 2022; originally announced July 2022.

Spin-defect characteristics of single sulfur vacancies in monolayer $\text{MoS}_2$

Authors: Alexander Hötger, Tomer Amit, Julian Klein, Katja Barthelmi, Thomas Pelini, Alex Delhomme, Sergio Rey, Marek Potemski, Clément Faugeras, Galit Cohen, Daniel Hernangómez-Pérez, Takashi Taniguchi, Kenji Watanabe, Christoph Kastl, Jonathan J. Finley, Sivan Refaely-Abramson, Alexander W. Holleitner, Andreas V. Stier

Abstract: Single spin defects in 2D transition-metal dichalcogenides are natural spin-photon interfaces for quantum applications. Here we report high-field magneto-photoluminescence spectroscopy from three emission lines (Q1, Q2 and Q*) of He-ion induced sulfur vacancies in monolayer $\text{MoS}_2$. Analysis of the asymmetric PL lineshapes in combination with the diamagnetic shift of Q1 and Q2 yields a cons… ▽ More Single spin defects in 2D transition-metal dichalcogenides are natural spin-photon interfaces for quantum applications. Here we report high-field magneto-photoluminescence spectroscopy from three emission lines (Q1, Q2 and Q*) of He-ion induced sulfur vacancies in monolayer $\text{MoS}_2$. Analysis of the asymmetric PL lineshapes in combination with the diamagnetic shift of Q1 and Q2 yields a consistent picture of localized emitters with a wavefunction extent of $\sim$ 3.5 nm. The distinct valley-Zeeman splitting in out-of-plane $B$-fields and the brightening of dark states through in-plane $B$-fields necessitates spin-valley selectivity of the defect states and lifted spin-degeneracy at zero field. Comparing our results to ab-initio calculations identifies the nature of Q1 and Q2 and suggests that Q* is the emission from a chemically functionalized defect. Analysis of the optical degree of circular polarization reveals that the Fermi level is a parameter that enables the tunability of the emitter. These results show that defects in 2D semiconductors may be utilized for quantum technologies. △ Less

Submitted 17 March, 2023; v1 submitted 20 May, 2022; originally announced May 2022.

Journal ref: npj 2D Mater. Appl. 7, 30 (2023)

Tunable magneto-optical properties in MoS$_2$ via defect-induced exciton transitions

Authors: Tomer Amit, Daniel Hernangómez-Pérez, Galit Cohen, Diana Y. Qiu, Sivan Refaely-Abramson

Abstract: The presence of chalcogen vacancies in monolayer transition metal dichalcogenides (TMDs) leads to excitons with mixed localized-delocalized character and to reduced valley selectivity. Recent experimental advances in defect design in TMDs allow for a close examination of such mixed exciton states as a function of their degree of circular polarization under external magnetic fields, revealing stron… ▽ More The presence of chalcogen vacancies in monolayer transition metal dichalcogenides (TMDs) leads to excitons with mixed localized-delocalized character and to reduced valley selectivity. Recent experimental advances in defect design in TMDs allow for a close examination of such mixed exciton states as a function of their degree of circular polarization under external magnetic fields, revealing strongly varying defect-induced magnetic properties. A theoretical understanding of these observations and their physical origins demands a predictive, structure-sensitive theory. In this work, we study the effect of chalcogen vacancies on the exciton magnetic properties in monolayer MoS$_2$. Using many-body perturbation theory, we show how the complex excitonic picture associated with the presence of defects -- with reduced valley and spin selectivity due to hybridized electron-hole transitions -- leads to structurally-controllable exciton magnetic response. We find a variety of g-factors with changing magnitudes and sign depending on the exciton energy and character. Our findings suggest a pathway to tune the nature of the excitons -- and by that their magneto-optical properties -- through defect architecture. △ Less

Submitted 26 March, 2022; originally announced March 2022.

Journal ref: Phys. Rev. B 106, L161407 (2022)

Interaction expansion inchworm Monte Carlo solver for lattice and impurity models

Authors: Jia Li, Yang Yu, Emanuel Gull, Guy Cohen

Abstract: Multi-orbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to a few impurity orbitals, discretized baths, diagonal hybridizations, or density-density interactions. Here, we generalize the inchworm quantum Monte Carlo metho… ▽ More Multi-orbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to a few impurity orbitals, discretized baths, diagonal hybridizations, or density-density interactions. Here, we generalize the inchworm quantum Monte Carlo method to the interaction expansion and explore its application to typical single- and multi-orbital problems encountered in investigations of impurity and lattice models. Our implementation generically outperforms bare and bold-line quantum Monte Carlo algorithms in the interaction expansion. So far, for the systems studied here, it remains inferior to the more specialized hybridization expansion and auxiliary field algorithms. The problem of convergence to unphysical fixed points, which hampers so-called bold-line methods, is not encountered in inchworm Monte Carlo. △ Less

Submitted 9 January, 2022; originally announced January 2022.

Journal ref: Phys. Rev. B 105, 165133 (2022)

Reduced Dynamics of Full Counting Statistics

Authors: Felix A. Pollock, Emanuel Gull, K. Modi, Guy Cohen

Abstract: We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they can be difficult to formulate for observables spanning the system and its environment, such as those characterizing transport properties. A large variety of mix… ▽ More We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they can be difficult to formulate for observables spanning the system and its environment, such as those characterizing transport properties. A large variety of mixed system--environment observables, as well as their statistical properties, can be evaluated by considering counting fields. Given a numerical method able to simulate the field-modified dynamics over the memory timescale, we show that the long-lived full counting statistics can be efficiently obtained from the reduced dynamics. We demonstrate the utility of the technique by computing the long-time current in the nonequilibrium Anderson impurity model from short-time Monte Carlo simulations. △ Less

Submitted 19 May, 2022; v1 submitted 16 November, 2021; originally announced November 2021.

Journal ref: SciPost Phys. 13, 027 (2022)

The Kondo Cloud in a 1D Nanowire

Authors: Joseph Kleinhenz, Igor Krivenko, Guy Cohen, Emanuel Gull

Abstract: A recent experiment [Nature 579, 210--213 (2020)] probed the extent of the Kondo cloud in 1D by measuring the effect of electrostatic perturbations applied a distance $L$ away from the impurity on $T_K$. We study the Kondo cloud in a model proposed to describe this experimental setup, consisting of a single impurity Anderson model coupled to two semi-infinite 1D leads. In agreement with the experi… ▽ More A recent experiment [Nature 579, 210--213 (2020)] probed the extent of the Kondo cloud in 1D by measuring the effect of electrostatic perturbations applied a distance $L$ away from the impurity on $T_K$. We study the Kondo cloud in a model proposed to describe this experimental setup, consisting of a single impurity Anderson model coupled to two semi-infinite 1D leads. In agreement with the experimental results, we find that $T_K$ is strongly affected by perturbations to the lead within the Kondo cloud. We obtain a complementary picture of the Kondo cloud in this system by observing how the Kondo state manifests itself in the local density of states of the leads, which may be observed experimentally via scanning tunneling microscopy. Our results support the existing experimental data and provide detailed predictions for future experiments seeking to characterize the Kondo cloud in this system. △ Less

Submitted 18 June, 2021; originally announced June 2021.

Heavily Doped Semiconductor Nanocrystal Quantum Dots

Authors: David Mocatta, Guy Cohen, Jonathan Schattner, Oded Millo, Eran Rabani, Uri Banin

Abstract: Doping of semiconductors by impurity atoms enabled their widespread technological application in micro and opto-electronics. For colloidal semiconductor nanocrystals, an emerging family of materials where size, composition and shape-control offer widely tunable optical and electronic properties, doping has proven elusive. This arises both from the synthetic challenge of how to introduce single imp… ▽ More Doping of semiconductors by impurity atoms enabled their widespread technological application in micro and opto-electronics. For colloidal semiconductor nanocrystals, an emerging family of materials where size, composition and shape-control offer widely tunable optical and electronic properties, doping has proven elusive. This arises both from the synthetic challenge of how to introduce single impurities and from a lack of fundamental understanding of this heavily doped limit under strong quantum confinement. We develop a method to dope semiconductor nanocrystals with metal impurities providing control of the band gap and Fermi energy. A combination of optical measurements, scanning tunneling spectroscopy and theory revealed the emergence of a confined impurity band and band-tailing. Successful control of doping and its understanding provide n- and p-doped semiconductor nanocrystals which greatly enhance the potential application of such materials in solar cells, thin-film transistors, and optoelectronic devices. △ Less

Submitted 23 May, 2021; originally announced May 2021.

Comments: Paper - 17 pages, 4 figures SI - 3 pages, 24 figures

Journal ref: Science 01 Apr 2011, Vol. 332, Issue 6025, pp. 77-81

Signatures of Dimensionality and Symmetry in Exciton Bandstructure: Consequences for Time-Evolution

Authors: Diana Y. Qiu, Galit Cohen, Dana Novichkova, Sivan Refaely-Abramson

Abstract: Exciton dynamics, lifetimes and scattering are directly related to the exciton dispersion, or bandstructure. While electron and phonon bandstructures are well understood and can be easily calculated from first principles, the exciton bandstructure is commonly conflated with the underlying electronic bandstructure, where the exciton dispersion is assumed to follow the same dispersion as the electro… ▽ More Exciton dynamics, lifetimes and scattering are directly related to the exciton dispersion, or bandstructure. While electron and phonon bandstructures are well understood and can be easily calculated from first principles, the exciton bandstructure is commonly conflated with the underlying electronic bandstructure, where the exciton dispersion is assumed to follow the same dispersion as the electron and hole bands from which it is composed (i.e., the effective mass model). Here, we present a general theory of exciton bandstructure within both ab initio and model Hamiltonian approaches. We show that contrary to common assumption, the exciton bandstructure contains non-analytical discontinuities -- a feature which is impossible to obtain from the electronic bandstructure alone. These discontinuities are purely quantum phenomena, arising from the exchange scattering of electron-hole pairs. We show that the degree of these discontinuities depends on materials' symmetry and dimensionality, with jump discontinuities occurring in 3D and different orders of removable discontinuities in 2D and 1D. We connect these unexpected features to the early stages of exciton dynamics, which shows remarkable correspondence with recent experimental observations and suggests that the measured diffusion patterns are influenced by the underlying exciton bandstructure. △ Less

Submitted 12 March, 2021; originally announced March 2021.

Resolving the nonequilibrium Kondo singlet in energy- and position-space using quantum measurements

Authors: André Erpenbeck, Guy Cohen

Abstract: The Kondo effect, a hallmark of strong correlation physics, is characterized by the formation of an extended cloud of singlet states around magnetic impurities at low temperatures. While many implications of the Kondo cloud's existence have been verified, the existence of the singlet cloud itself has not been directly demonstrated. We suggest a route for such a demonstration by considering an obse… ▽ More The Kondo effect, a hallmark of strong correlation physics, is characterized by the formation of an extended cloud of singlet states around magnetic impurities at low temperatures. While many implications of the Kondo cloud's existence have been verified, the existence of the singlet cloud itself has not been directly demonstrated. We suggest a route for such a demonstration by considering an observable that has no classical analog, but is still experimentally measurable: "singlet weights", or projections onto particular entangled two-particle states. Using approximate theoretical arguments, we show that it is possible to construct highly specific energy- and position-resolved probes of Kondo correlations. Furthermore, we consider a quantum transport setup that can be driven away from equilibrium by a bias voltage. There, we show that singlet weights are enhanced by voltage even as the Kondo effect is weakened by it. This exposes a patently nonequilibrium mechanism for the generation of Kondo-like entanglement that is inherently different from its equilibrium counterpart. △ Less

Submitted 25 June, 2021; v1 submitted 24 December, 2020; originally announced December 2020.

Comments: 16 pages, 7 figures

Journal ref: SciPost Phys. 10, 142 (2021)

Revealing strong correlations in higher order transport statistics: a noncrossing approximation approach

Authors: André Erpenbeck, Emanuel Gull, Guy Cohen

Abstract: We present a method for calculating the full counting statistics of a nonequilibrium quantum system based on the propagator noncrossing approximation (NCA). This numerically inexpensive method can provide higher order cumulants for extended parameter regimes, rendering it attractive for a wide variety of purposes. We compare NCA results to Born-Markov quantum master equations (QME) results to show… ▽ More We present a method for calculating the full counting statistics of a nonequilibrium quantum system based on the propagator noncrossing approximation (NCA). This numerically inexpensive method can provide higher order cumulants for extended parameter regimes, rendering it attractive for a wide variety of purposes. We compare NCA results to Born-Markov quantum master equations (QME) results to show that they can access different physics, and to numerically exact inchworm quantum Monte-Carlo data to assess their validity. As a demonstration of its power, the NCA method is employed to study the impact of correlations on higher order cumulants in the nonequilibrium Anderson impurity model. The four lowest order cumulants are examined, allowing us to establish that correlation effects have a profound influence on the underlying transport distributions. Higher order cumulants are therefore demonstrated to be a proxy for the presence of Kondo correlations in a way that cannot be captured by simple QME methods. △ Less

Submitted 31 March, 2021; v1 submitted 7 October, 2020; originally announced October 2020.

Journal ref: Phys. Rev. B 103, 125431 (2021)

Dynamic Control of Nonequilibrium Metal-Insulator Transitions

Authors: Joseph Kleinhenz, Igor Krivenko, Guy Cohen, Emanuel Gull

Abstract: We demonstrate a first order metal-insulator phase transition in the repulsive, fully frustrated, single-band Hubbard model as a function of the coupling to a fermion bath. Time dependent manipulation of the bath coupling allows switching between metallic and insulating states both across the phase transition and within the coexistence region. We propose a simple nanoelectronic device for experime… ▽ More We demonstrate a first order metal-insulator phase transition in the repulsive, fully frustrated, single-band Hubbard model as a function of the coupling to a fermion bath. Time dependent manipulation of the bath coupling allows switching between metallic and insulating states both across the phase transition and within the coexistence region. We propose a simple nanoelectronic device for experimentally realizing dynamic control of the bath coupling. Analysis of the device characteristics shows that it can act as a two-terminal memristor. △ Less

Submitted 9 April, 2020; originally announced April 2020.

How moving cracks in brittle solids choose their path

Authors: Lital Rozen-Levy, John M. Kolinski, Gil Cohen, Jay Fineberg

Abstract: While we fundamentally understand the dynamics of 'simple' cracks propagating in brittle solids within perfect (homogeneous) materials, we do not understand how paths of moving cracks are determined. We experimentally study strongly perturbed cracks that propagate between 10-95\% of their limiting velocity within a brittle material. These cracks are deflected by either interaction with sparsely im… ▽ More While we fundamentally understand the dynamics of 'simple' cracks propagating in brittle solids within perfect (homogeneous) materials, we do not understand how paths of moving cracks are determined. We experimentally study strongly perturbed cracks that propagate between 10-95\% of their limiting velocity within a brittle material. These cracks are deflected by either interaction with sparsely implanted defects or via an intrinsic oscillatory instability in defect-free media. Dense, high-speed measurements of the strain fields surrounding the crack tips reveal that crack paths are governed by the direction of maximal strain energy density. This fundamentally important result may be utilized to either direct or guide running cracks. △ Less

Submitted 10 September, 2020; v1 submitted 7 April, 2020; originally announced April 2020.

Comments: J.F., L. L-R, and G.C. acknowledge the support of Israel Science Foundation (grants 1523/15 and 840/19). J.M.K. and L. L-R. contributed equally to this work

Journal ref: Phys. Rev. Lett. 125, 175501 (2020)

Green's function methods for single molecule junctions

Authors: Guy Cohen, Michael Galperin

Abstract: We present a brief pedagogical review of theoretical Green's function methods applicable to open quantum systems out of equilibrium in general, and single molecule junctions in particular. We briefly describe experimental advances in molecular electronics, then discuss different theoretical approaches. We then focus on Green's function methods. Two characteristic energy scales governing the physic… ▽ More We present a brief pedagogical review of theoretical Green's function methods applicable to open quantum systems out of equilibrium in general, and single molecule junctions in particular. We briefly describe experimental advances in molecular electronics, then discuss different theoretical approaches. We then focus on Green's function methods. Two characteristic energy scales governing the physics are many-body interactions within the junctions, and molecule-contact coupling. We therefore discuss weak interactions and weak coupling, as two limits that can be conveniently treated within, respectively, the standard nonequilibrium Green's function (NEGF) method and its many-body flavors (pseudoparticle and Hubbard NEGF). We argue that the intermediate regime, where the two energy scales are comparable, can in many cases be efficiently treated within the recently introduced superperturbation dual fermion approach. Finally, we review approaches for going beyond these analytically accessible limits, as embodied by recent developments in numerically exact methods based on Green's functions. △ Less

Submitted 7 March, 2020; v1 submitted 16 January, 2020; originally announced January 2020.

Comments: Perspective. 25 pages, 8 figures

Journal ref: J. Chem. Phys. 152, 090901 (2020)

Correlated nonequilibrium steady states without energy flux

Authors: Hristiana Atanasova, Alexander I. Lichtenstein, Guy Cohen

Abstract: Floquet engineering of closed quantum systems can lead to the formation of long-lived prethermal states that, in general, eventually thermalize to infinite temperature. Coupling these driven systems to dissipative baths can stabilize such states, establishing a true nonequilibrium steady state. We demonstrate that in a certain strongly interacting lattice model coupled to a bath and driven by an e… ▽ More Floquet engineering of closed quantum systems can lead to the formation of long-lived prethermal states that, in general, eventually thermalize to infinite temperature. Coupling these driven systems to dissipative baths can stabilize such states, establishing a true nonequilibrium steady state. We demonstrate that in a certain strongly interacting lattice model coupled to a bath and driven by an electric field, such steady states can have the remarkable property that the cycle-averaged rate of energy transfer between the lattice and the baths vanishes. Despite this, we show that these states retain a clear nonequilibrium nature. △ Less

Submitted 1 June, 2020; v1 submitted 6 October, 2019; originally announced October 2019.

Journal ref: Phys. Rev. B 101, 174316 (2020)

Dynamic fields at the tip of sub-Rayleigh and supershear frictional rupture fronts

Authors: Ilya Svetlizky, Gabriele Albertini, Gil Cohen, David S. Kammer, Jay Fineberg

Abstract: The onset of frictional motion at the interface between two distinct bodies in contact is characterized by the propagation of dynamic rupture fronts. We combine friction experiments and numerical simulations to study the properties of these frictional rupture fronts. We extend previous analysis of slow and sub-Rayleigh rupture fronts and show that strain fields and the evolution of real contact ar… ▽ More The onset of frictional motion at the interface between two distinct bodies in contact is characterized by the propagation of dynamic rupture fronts. We combine friction experiments and numerical simulations to study the properties of these frictional rupture fronts. We extend previous analysis of slow and sub-Rayleigh rupture fronts and show that strain fields and the evolution of real contact area in the tip vicinity of supershear ruptures are well described by analytical fracture-mechanics solutions. Fracture-mechanics theory further allows us to determine long sought-after interface properties, such as local fracture energy and frictional peak strength. Both properties are observed to be roughly independent of rupture speed and mode of propagation. However, our study also reveals discrepancies between measurements and analytical solutions that appear as the rupture speed approaches the longitudinal wave speed. Further comparison with dynamic simulations illustrates that, in the supershear propagation regime, transient and geometrical (finite sample thickness) effects cause smaller near-tip strain amplitudes than expected from the fracture-mechanics theory. By showing good quantitative agreement between experiments, simulations and theory over the entire range of possible rupture speeds, we demonstrate that frictional rupture fronts are classic dynamic cracks despite residual friction. △ Less

Submitted 31 January, 2020; v1 submitted 27 August, 2019; originally announced August 2019.

Comments: 20 pages including 11 figures

Numerically exact counting statistics of energy current in the Kondo regime

Authors: Michael Ridley, Michael Galperin, Emanuel Gull, Guy Cohen

Abstract: We use the inchworm Quantum Monte Carlo method to investigate the full counting statistics of particle and energy currents in a strongly correlated quantum dot. Our method is used to extract the heat fluctuations and entropy production of a quantum thermoelectric device, as well as cumulants of the particle and energy currents. The energy--particle current cross correlations reveal information on… ▽ More We use the inchworm Quantum Monte Carlo method to investigate the full counting statistics of particle and energy currents in a strongly correlated quantum dot. Our method is used to extract the heat fluctuations and entropy production of a quantum thermoelectric device, as well as cumulants of the particle and energy currents. The energy--particle current cross correlations reveal information on the preparation of the system and the interplay of thermal and electric currents. We furthermore demonstrate the signature of a crossover from Coulomb blockade to Kondo physics in the energy current fluctuations, and show how the conventional master equation approach to full counting statistics systematically fails to capture this crossover. △ Less

Submitted 22 July, 2019; originally announced July 2019.

Journal ref: Phys. Rev. B 100, 165127 (2019)

Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations

Authors: Eitan Eidelstein, Emanuel Gull, Guy Cohen

Abstract: We present a numerically exact Inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign problem in certain real-time propagation problems, can also overcome the sign problem as a function of temperature for equilibrium quantum impurity models. This is… ▽ More We present a numerically exact Inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign problem in certain real-time propagation problems, can also overcome the sign problem as a function of temperature for equilibrium quantum impurity models. This is shown in several cases where the current method of choice, the continuous-time hybridization expansion, fails due to the sign problem. Our method therefore enables simulations of impurity problems as they appear in embedding theories without further approximations, such as the truncation of the hybridization or interaction structure or a discretization of the impurity bath with a set of discrete energy levels, and eliminates a crucial bottleneck in the simulation of ab initio embedding problems. △ Less

Submitted 22 May, 2020; v1 submitted 19 July, 2019; originally announced July 2019.

Journal ref: Phys. Rev. Lett. 124, 206405 (2020)

Dynamics of Kondo voltage splitting after a quantum quench

Authors: Igor Krivenko, Joseph Kleinhenz, Guy Cohen, Emanuel Gull

Abstract: We analyze the time-dependent formation of the spectral function of an Anderson impurity model in the Kondo regime within a numerically exact real-time quantum Monte Carlo framework. At steady state, splitting of the Kondo peak occurs with nontrivial dependence on voltage and temperature, and with little effect on the location or intensity of high-energy features. Examining the transient developme… ▽ More We analyze the time-dependent formation of the spectral function of an Anderson impurity model in the Kondo regime within a numerically exact real-time quantum Monte Carlo framework. At steady state, splitting of the Kondo peak occurs with nontrivial dependence on voltage and temperature, and with little effect on the location or intensity of high-energy features. Examining the transient development of the Kondo peak after a quench from an initially uncorrelated state reveals a two-stage process where the initial formation of a single central Kondo peak is followed by splitting. We analyze the time dependence of splitting in detail and demonstrate a strong dependence of its characteristic timescale on the voltage. We expect both the steady state and the transient phenomenon to be experimentally observable. △ Less

Submitted 15 November, 2019; v1 submitted 25 April, 2019; originally announced April 2019.

Comments: 6 pages, 4 figures

Journal ref: Phys. Rev. B 100, 201104 (2019)

Lead Geometry and Transport Statistics in Molecular Junctions

Authors: Michael Ridley, Emanuel Gull, Guy Cohen

Abstract: We present a numerically exact study of charge transport and its fluctuations through a molecular junction driven out of equilibrium by a bias voltage, using the Inchworm quantum Monte Carlo (iQMC) method. After showing how the technique can be used to address any lead geometry, we concentrate on one dimensional chains as an example. The finite bandwidth of the leads is shown to affect transport p… ▽ More We present a numerically exact study of charge transport and its fluctuations through a molecular junction driven out of equilibrium by a bias voltage, using the Inchworm quantum Monte Carlo (iQMC) method. After showing how the technique can be used to address any lead geometry, we concentrate on one dimensional chains as an example. The finite bandwidth of the leads is shown to affect transport properties in ways that cannot be fully captured by quantum master equations: in particular, we reveal an interaction-induced broadening of transport channels that is visible at all voltages, and show how fluctuations of the current are a more sensitive probe of this effect than the mean current. △ Less

Submitted 26 June, 2019; v1 submitted 18 March, 2019; originally announced March 2019.

Journal ref: J. Chem. Phys. 150, 244107 (2019)

Auxiliary master equation for nonequilibrium dual-fermion approach

Authors: Feng Chen, Guy Cohen, Michael Galperin

Abstract: We introduce auxiliary quantum master equation - dual fermion approach (QME-DF) and argue that it presents a convenient way to describe steady-states of correlated impurity systems. The combined scheme yields an expansion around a reference much closer to the true nonequilibrium state than in the original dual fermion formulation. In steady-state situations, the scheme is numerically cheaper and a… ▽ More We introduce auxiliary quantum master equation - dual fermion approach (QME-DF) and argue that it presents a convenient way to describe steady-states of correlated impurity systems. The combined scheme yields an expansion around a reference much closer to the true nonequilibrium state than in the original dual fermion formulation. In steady-state situations, the scheme is numerically cheaper and allows to avoid long time propagation of previous considerations. Anderson impurity is used as a test model. The QME-DF simulations are compared with numerically exact tdDMRG results. △ Less

Submitted 24 October, 2018; originally announced October 2018.

Comments: 8 pages, 4 figures

Journal ref: Phys. Rev. Lett. 122, 186803 (2019)

Inclusion-Exclusion Principle for Many-Body Diagrammatics

Authors: Aviel Boag, Emanuel Gull, Guy Cohen

Abstract: Recent successes in Monte Carlo methods for simulating fermionic quantum impurity models have been based on diagrammatic resummation techniques, but are restricted by the need to sum over factorially large classes of diagrams individually. We present a fast algorithm for summing over the diagrams appearing in Inchworm hybridization expansions. The method relies on the inclusion-exclusion principle… ▽ More Recent successes in Monte Carlo methods for simulating fermionic quantum impurity models have been based on diagrammatic resummation techniques, but are restricted by the need to sum over factorially large classes of diagrams individually. We present a fast algorithm for summing over the diagrams appearing in Inchworm hybridization expansions. The method relies on the inclusion-exclusion principle to reduce the scaling from factorial to exponential. We analyze the growth rate and compare with related algorithms for expansions in the many-body interaction. An implementation demonstrates that for a simulation of a concrete physical model at reasonable parameters and accuracy, our algorithm not only scales better asymptotically, but also provides performance gains of approximately two orders of magnitude in practice over the previous state-of-the-art. △ Less

Submitted 1 July, 2018; originally announced July 2018.

Journal ref: Phys. Rev. B 98, 115152 (2018)

Numerically exact full counting statistics of the nonequilibrium Anderson impurity model

Authors: Michael Ridley, Viveka Nand Singh, Emanuel Gull, Guy Cohen

Abstract: The time dependent full counting statistics of charge transport through an interacting quantum junction is evaluated from its generating function, controllably computed with the inchworm Monte Carlo method. Exact noninteracting results are reproduced; then, we continue to explore the effect of electron--electron interactions on the time-dependent charge cumulants, first-passage time distributions… ▽ More The time dependent full counting statistics of charge transport through an interacting quantum junction is evaluated from its generating function, controllably computed with the inchworm Monte Carlo method. Exact noninteracting results are reproduced; then, we continue to explore the effect of electron--electron interactions on the time-dependent charge cumulants, first-passage time distributions and $n$-electron transfer distributions. We observe a crossover in the noise from Coulomb blockade- to Kondo-dominated physics as the temperature is decreased. In addition, we uncover long-tailed spin distributions in the Kondo regime and analyze queuing behavior caused by correlations between single electron transfer events. △ Less

Submitted 15 January, 2018; originally announced January 2018.

Journal ref: Phys. Rev. B 97, 115109 (2018)

Topological defects govern crack front motion and facet formation on broken surfaces

Authors: Itamar Kolvin, Gil Cohen, Jay Fineberg

Abstract: Patterns on broken surfaces are well-known from everyday experience, but surprisingly, how and why they form are very much open questions. Well-defined facets are commonly observed1-4 along fracture surfaces which are created by slow tensile cracks. As facets appear in amorphous materials5-7, their formation does not reflect microscopic order. Fracture mechanics, however, predict that slow crack f… ▽ More Patterns on broken surfaces are well-known from everyday experience, but surprisingly, how and why they form are very much open questions. Well-defined facets are commonly observed1-4 along fracture surfaces which are created by slow tensile cracks. As facets appear in amorphous materials5-7, their formation does not reflect microscopic order. Fracture mechanics, however, predict that slow crack fronts should be straight, creating mirror-like surfaces8-13. In contrast, facet-forming fronts propagate simultaneously within different planes separated by steps. It is therefore unclear why steps are stable, what determines their path and how they couple to crack front dynamics. Here we show, by integrating real-time imaging of propagating crack fronts with surface measurements, that steps are topological defects of crack fronts; crack front separation into discontinuous overlapping segments provides the condition for step stability. Steps drift at a constant angle to the local front propagation direction and the increased local dissipation due to step formation couples to the long-range deformation of the surrounding crack fronts. Slow crack front dynamics are enslaved to changes in step heights and positions. These observations show how 3D topology couples to 2D fracture dynamics to provide a fundamental picture of how patterned surfaces are generated. △ Less

Submitted 6 August, 2017; originally announced August 2017.

Comments: 14 pages, 6 figures

Quantum Monte Carlo solution of the dynamical mean field equations in real time

Authors: Qiaoyuan Dong, Igor Krivenko, Joseph Kleinhenz, Andrey E. Antipov, Guy Cohen, Emanuel Gull

Abstract: We present real-time inchworm quantum Monte Carlo results for single-site dynamical mean field theory on an infinite coordination number Bethe lattice. Our numerically exact results are obtained on the L-shaped Keldysh contour and, being evaluated in real-time, avoid the analytic continuation issues typically encountered in Monte Carlo calculations. Our results show that inchworm Monte Carlo metho… ▽ More We present real-time inchworm quantum Monte Carlo results for single-site dynamical mean field theory on an infinite coordination number Bethe lattice. Our numerically exact results are obtained on the L-shaped Keldysh contour and, being evaluated in real-time, avoid the analytic continuation issues typically encountered in Monte Carlo calculations. Our results show that inchworm Monte Carlo methods have now reached a state where they can be used as dynamical mean field impurity solvers and the dynamical sign problem can be overcome. As non-equilibrium problems can be simulated at the same cost, we envisage the main use of these methods as dynamical mean field solvers for time-dependent problems far from equilibrium. △ Less

Submitted 9 June, 2017; originally announced June 2017.

Journal ref: Phys. Rev. B 96, 155126 (2017)

Nonequilibrium Langevin dynamics: a demonstration study of shear flow fluctuations in a simple fluid

Authors: Roman Belousov, E. G. D. Cohen, Lamberto Rondoni

Abstract: The present study is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the related deterministic parameters of the Langevin equation for a Couette flow in a microscopic Molecular Dynamics model of a simple fluid. In this paper we find all… ▽ More The present study is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the related deterministic parameters of the Langevin equation for a Couette flow in a microscopic Molecular Dynamics model of a simple fluid. In this paper we find all the remaining constants of the stochastic dynamics, which is then numerically simulated and directly compared with the original physical system. By using these data, we study in detail the accuracy and precision of a second-order Langevin model for nonequilibrium physical systems, theoretically and computationally. In addition, an intriguing relation is found between an applied external force and cumulants of the resulting flow fluctuations. This is characterized by a linear dependence of athermal cumulant ratio, a new quantity introduced here. △ Less

Submitted 16 May, 2017; originally announced May 2017.

Journal ref: Phys. Rev. E 96, 022125 (2017)

Inchworm Monte Carlo for exact non-adiabatic dynamics I. Theory and algorithms

Authors: Hsing-Ta Chen, Guy Cohen, David R. Reichman

Abstract: In this paper we provide a detailed description of the inchworm Monte Carlo formalism for the exact study of real-time non-adiabatic dynamics. This method optimally recycles Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. Using the example of the spin-boson model, we formulate the inchworm expansion in two distinct ways: The first with respect to an expan… ▽ More In this paper we provide a detailed description of the inchworm Monte Carlo formalism for the exact study of real-time non-adiabatic dynamics. This method optimally recycles Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. Using the example of the spin-boson model, we formulate the inchworm expansion in two distinct ways: The first with respect to an expansion in the system-bath coupling and the second as an expansion in the diabatic coupling. The latter approach motivates the development of a cumulant version of the inchworm Monte Carlo method, which has the benefit of improved scaling. This paper deals completely with methodology, while Paper II provides a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each. △ Less

Submitted 24 January, 2017; v1 submitted 29 October, 2016; originally announced October 2016.

Comments: 16 pages, 6 figures

Journal ref: J. Chem. Phys. 146, 054105 (2017)

Currents and Green's functions of impurities out of equilibrium -- results from inchworm Quantum Monte Carlo

Authors: Andrey E. Antipov, Qiaoyuan Dong, Joseph Kleinhenz, Guy Cohen, Emanuel Gull

Abstract: We generalize the recently developed inchworm quantum Monte Carlo method to the full Keldysh contour with forward, backward, and equilibrium branches to describe the dynamics of strongly correlated impurity problems with time dependent parameters. We introduce a method to compute Green's functions, spectral functions, and currents for inchworm Monte Carlo and show how systematic error assessments… ▽ More We generalize the recently developed inchworm quantum Monte Carlo method to the full Keldysh contour with forward, backward, and equilibrium branches to describe the dynamics of strongly correlated impurity problems with time dependent parameters. We introduce a method to compute Green's functions, spectral functions, and currents for inchworm Monte Carlo and show how systematic error assessments in real time can be obtained. We then illustrate the capabilities of the algorithm with a study of the behavior of quantum impurities after an instantaneous voltage quench from a thermal equilibrium state. △ Less

Submitted 29 October, 2016; originally announced October 2016.

Journal ref: Phys. Rev. B 95, 085144 (2017)

Inchworm Monte Carlo for exact non-adiabatic dynamics II. Benchmarks and comparison with established methods

Authors: Hsing-Ta Chen, Guy Cohen, David R. Reichman

Abstract: In this second paper of a two part series, we present extensive benchmark results for two different inchworm Monte Carlo expansions for the spin-boson model. Our results are compared to previously developed numerically exact approaches for this problem. A detailed discussion of convergence and error propagation is presented. Our results and analysis allow for an understanding of the benefits and d… ▽ More In this second paper of a two part series, we present extensive benchmark results for two different inchworm Monte Carlo expansions for the spin-boson model. Our results are compared to previously developed numerically exact approaches for this problem. A detailed discussion of convergence and error propagation is presented. Our results and analysis allow for an understanding of the benefits and drawbacks of inchworm Monte Carlo compared to other approaches for exact real-time non-adiabatic quantum dynamics. △ Less

Submitted 24 January, 2017; v1 submitted 28 October, 2016; originally announced October 2016.

Comments: 10 pages, 8 figures

Journal ref: J. Chem. Phys. 146, 054106 (2017)

Second-order fluctuation theory and time autocorrelation function for currents

Authors: Roman Belousov, E. G. D. Cohen

Abstract: By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating variables, including hydrodynamic currents, in equilibrium as well as nonequilibrium steady states. From the solution of the obtained stochastic equations we derive an a… ▽ More By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating variables, including hydrodynamic currents, in equilibrium as well as nonequilibrium steady states. From the solution of the obtained stochastic equations we derive an analytical expression for the time autocorrelation function of a general fluctuating quantity. This theoretical result is then tested in a study of a shear flow by molecular dynamics simulations. The proposed form of the time autocorrelation function yields an excellent fit to our computational data for both equilibrium and nonequilibrium steady states. Unlike the analogous result of the first-order Onsager-Machlup theory, our expression correctly describes the short-time correlations. Its utility is demonstrated in an application of the Green-Kubo formula for the transport coefficient. Curiously, the normalized time autocorrelation function for the shear flow, which only depends on the deterministic part of the fluctuation dynamics, appears independent of the external shear force in the linear nonequilibrium regime. △ Less

Submitted 14 October, 2016; originally announced October 2016.

Journal ref: Phys. Rev. E 94, 062124 (2016)