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Deep learning lattice gauge theories
Authors:
Anuj Apte,
Anthony Ashmore,
Clay Cordova,
Tzu-Chen Huang
Abstract:
Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last four decades, fundamental challenges such as the sign problem and the inability to simulate real-time dynamics remain. Neural network quantum states have emerg…
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Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last four decades, fundamental challenges such as the sign problem and the inability to simulate real-time dynamics remain. Neural network quantum states have emerged as an alternative method that seeks to overcome these challenges. In this work, we use gauge-invariant neural network quantum states to accurately compute the ground state of $\mathbb{Z}_N$ lattice gauge theories in $2+1$ dimensions. Using transfer learning, we study the distinct topological phases and the confinement phase transition of these theories. For $\mathbb{Z}_2$, we identify a continuous transition and compute critical exponents, finding excellent agreement with existing numerics for the expected Ising universality class. In the $\mathbb{Z}_3$ case, we observe a weakly first-order transition and identify the critical coupling. Our findings suggest that neural network quantum states are a promising method for precise studies of lattice gauge theory.
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Submitted 12 July, 2025; v1 submitted 23 May, 2024;
originally announced May 2024.
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Obstructions to Gapped Phases from Non-Invertible Symmetries
Authors:
Anuj Apte,
Clay Cordova,
Ho Tat Lam
Abstract:
Quantum systems in 3+1-dimensions that are invariant under gauging a one-form symmetry enjoy novel non-invertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain dynamics. We show that such non-invertible symmetries often forbid a symmetry-preserving vacuum state with a gapped spectrum. In particular, we prove that a self-dua…
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Quantum systems in 3+1-dimensions that are invariant under gauging a one-form symmetry enjoy novel non-invertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain dynamics. We show that such non-invertible symmetries often forbid a symmetry-preserving vacuum state with a gapped spectrum. In particular, we prove that a self-dual theory with $\mathbb{Z}_{N}^{(1)}$ one-form symmetry is gapless or spontaneously breaks the self-duality symmetry unless $N=k^{2}\ell$ where $-1$ is a quadratic residue modulo $\ell$. We also extend these results to non-invertible symmetries arising from invariance under more general gauging operations including e.g. triality symmetries. Along the way, we discover how duality defects in symmetry protected topological phases have a hidden time-reversal symmetry that organizes their basic properties. These non-invertible symmetries are realized in lattice gauge theories, which serve to illustrate our results.
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Submitted 30 December, 2022;
originally announced December 2022.
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Non-Convex Optimization by Hamiltonian Alternation
Authors:
Anuj Apte,
Kunal Marwaha,
Arvind Murugan
Abstract:
A major obstacle to non-convex optimization is the problem of getting stuck in local minima. We introduce a novel metaheuristic to handle this issue, creating an alternate Hamiltonian that shares minima with the original Hamiltonian only within a chosen energy range. We find that repeatedly minimizing each Hamiltonian in sequence allows an algorithm to escape local minima. This technique is partic…
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A major obstacle to non-convex optimization is the problem of getting stuck in local minima. We introduce a novel metaheuristic to handle this issue, creating an alternate Hamiltonian that shares minima with the original Hamiltonian only within a chosen energy range. We find that repeatedly minimizing each Hamiltonian in sequence allows an algorithm to escape local minima. This technique is particularly straightforward when the ground state energy is known, and one obtains an improvement even without this knowledge. We demonstrate this technique by using it to find the ground state for instances of a Sherrington-Kirkpatrick spin glass.
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Submitted 28 June, 2022;
originally announced June 2022.
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Topological Signatures in Nodal Semimetals through Neutron Scattering
Authors:
Thanh Nguyen,
Yoichiro Tsurimaki,
Ricardo Pablo-Pedro,
Grigory Bednik,
Tongtong Liu,
Anuj Apte,
Nina Andrejevic,
Mingda Li
Abstract:
Topological nodal semimetals are known to host a variety of fascinating electronic properties due to the topological protection of the band-touching nodes. Neutron scattering, despite its power in probing elementary excitations, has not been routinely applied to topological semimetals, mainly due to the lack of an explicit connection between the neutron response and the signature of topology. In t…
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Topological nodal semimetals are known to host a variety of fascinating electronic properties due to the topological protection of the band-touching nodes. Neutron scattering, despite its power in probing elementary excitations, has not been routinely applied to topological semimetals, mainly due to the lack of an explicit connection between the neutron response and the signature of topology. In this work, we theoretically investigate the role that neutron scattering can play to unveil the topological nodal features: a large magnetic neutron response with spectral non-analyticity can be generated solely from the nodal bands. A new formula for the dynamical structure factor for generic topological nodal metals is derived. For Weyl semimetals, we show that the locations of Weyl nodes, the Fermi velocities and the signature of chiral anomaly can all leave hallmark neutron spectral responses. Our work offers a neutron-based avenue towards probing bulk topological materials.
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Submitted 10 January, 2022; v1 submitted 11 January, 2021;
originally announced January 2021.
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Thermalization of local observables in the $α$-FPUT chain
Authors:
Santhosh Ganapa,
Amit Apte,
Abhishek Dhar
Abstract:
Most studies on the problem of equilibration of the Fermi-Pasta-Ulam-Tsingou (FPUT) system have focused on equipartition of energy being attained amongst the normal modes of the corresponding harmonic system. In the present work, we instead discuss the equilibration problem in terms of local variables, and consider initial conditions corresponding to spatially localized energy. We estimate the tim…
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Most studies on the problem of equilibration of the Fermi-Pasta-Ulam-Tsingou (FPUT) system have focused on equipartition of energy being attained amongst the normal modes of the corresponding harmonic system. In the present work, we instead discuss the equilibration problem in terms of local variables, and consider initial conditions corresponding to spatially localized energy. We estimate the time-scales for equipartition of space localized degrees of freedom and find significant differences with the times scales observed for normal modes. Measuring thermalization in classical systems necessarily requires some averaging, and this could involve one over initial conditions or over time or spatial averaging. Here we consider averaging over initial conditions chosen from a narrow distribution in phase space. We examine in detail the effect of the width of the initial phase space distribution, and of integrability and chaos, on the time scales for thermalization. We show how thermalization properties of the system, quantified by its equilibration time, defined in this work, can be related to chaos, given by the maximal Lyapunov exponent. Somewhat surprisingly we also find that the ensemble averaging can lead to thermalization of the integrable Toda chain, though on much longer time scales.
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Submitted 29 June, 2020; v1 submitted 9 November, 2019;
originally announced November 2019.
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Topological Singularity Induced Chiral Kohn Anomaly in a Weyl Semimetal
Authors:
Thanh Nguyen,
Fei Han,
Nina Andrejevic,
Ricardo Pablo-Pedro,
Anuj Apte,
Yoichiro Tsurimaki,
Zhiwei Ding,
Kunyan Zhang,
Ahmet Alatas,
Ercan E. Alp,
Songxue Chi,
Jaime Fernandez-Baca,
Masaaki Matsuda,
David Alan Tennant,
Yang Zhao,
Zhijun Xu,
Jeffrey W. Lynn,
Shengxi Huang,
Mingda Li
Abstract:
The electron-phonon interaction (EPI) is instrumental in a wide variety of phenomena in solid-state physics, such as electrical resistivity in metals, carrier mobility, optical transition and polaron effects in semiconductors, lifetime of hot carriers, transition temperature in BCS superconductors, and even spin relaxation in diamond nitrogen-vacancy centers for quantum information processing. How…
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The electron-phonon interaction (EPI) is instrumental in a wide variety of phenomena in solid-state physics, such as electrical resistivity in metals, carrier mobility, optical transition and polaron effects in semiconductors, lifetime of hot carriers, transition temperature in BCS superconductors, and even spin relaxation in diamond nitrogen-vacancy centers for quantum information processing. However, due to the weak EPI strength, most phenomena have focused on electronic properties rather than on phonon properties. One prominent exception is the Kohn anomaly, where phonon softening can emerge when the phonon wavevector nests the Fermi surface of metals. Here we report a new class of Kohn anomaly in a topological Weyl semimetal (WSM), predicted by field-theoretical calculations, and experimentally observed through inelastic x-ray and neutron scattering on WSM tantalum phosphide (TaP). Compared to the conventional Kohn anomaly, the Fermi surface in a WSM exhibits multiple topological singularities of Weyl nodes, leading to a distinct nesting condition with chiral selection, a power-law divergence, and non-negligible dynamical effects. Our work brings the concept of Kohn anomaly into WSMs and sheds light on elucidating the EPI mechanism in emergent topological materials.
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Submitted 15 May, 2020; v1 submitted 2 June, 2019;
originally announced June 2019.
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Dynamical instability causes the demise of a supercooled tetrahedral liquid
Authors:
Arvind Kumar Gautam,
Nandlal Pingua,
Aashish Goyal,
Pankaj A. Apte
Abstract:
We investigate the relaxation mechanism of a supercooled tetrahedral liquid at its limit of stability using isothermal isobaric ($NPT$) Monte Carlo (MC) simulations. In similarity with systems which are far from equilibrium but near the onset of jamming [O'Hern et.al., Phys. Rev. Lett. {\bf 93}, 165702 (2004)], we find that the relaxation is characterized by two time-scales: the decay of long-wave…
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We investigate the relaxation mechanism of a supercooled tetrahedral liquid at its limit of stability using isothermal isobaric ($NPT$) Monte Carlo (MC) simulations. In similarity with systems which are far from equilibrium but near the onset of jamming [O'Hern et.al., Phys. Rev. Lett. {\bf 93}, 165702 (2004)], we find that the relaxation is characterized by two time-scales: the decay of long-wavelength (slow) fluctuations of potential energy is controlled by the the slope $[\partial (G/N)/\partial φ]$ of the Gibbs free energy ($G$) at a unique value of per particle potential energy $φ= φ_{mid}$. The short-wavelength (fast) fluctuations are controlled by the bath temperature $T$. The relaxation of the supercooled liquid is initiated with a dynamical crossover after which the potential energy fluctuations are biased towards values progressively lesser than $φ_{mid}$. The dynamical crossover leads to the change of time-scale, i.e., the decay of long-wavelength potential energy fluctuations (intermediate relaxation). Because of the condition [$\partial^2 (G/N)/\partial φ^2 = 0$] at $φ= φ_{mid}$, the slope $[\partial (G/N)/\partial φ]$ has a unique value and governs the intermediate stage of relaxation, which ends just after the crossover. In the subsequent stage, there is a relatively rapid crystallization due to lack of long-wavelength fluctuations and the instability at $φ_{mid}$, i.e., the condition that $G$ decreases as configurations with potential energies lower than $φ_{mid}$ are accessed. The dynamical crossover point and the associated change in the time-scale of fluctuations is found to be consistent with the previous studies.
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Submitted 14 August, 2017;
originally announced August 2017.
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Quaternary two-dimensional (2D) transition metal dichalcogenides (TMDs) with tunable bandgap
Authors:
Sandhya Susarla,
Alex Kutana,
Jordan A. Hachtel,
Vidya Kochat,
Amey Apte,
Robert Vajtai,
Juan Carlos Idrobo,
Boris I. Yakobson,
Chandra Sekhar Tiwary,
Pulickel M Ajayan
Abstract:
Alloying/doping in two-dimensional material has been important due to wide range band gap tunability. Increasing the number of components would increase the degree of freedom which can provide more flexibility in tuning the band gap and also reduced the growth temperature. Here, we report synthesis of quaternary alloys MoxW1-xS2ySe2(1-y) using chemical vapour deposition. The composition of alloys…
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Alloying/doping in two-dimensional material has been important due to wide range band gap tunability. Increasing the number of components would increase the degree of freedom which can provide more flexibility in tuning the band gap and also reduced the growth temperature. Here, we report synthesis of quaternary alloys MoxW1-xS2ySe2(1-y) using chemical vapour deposition. The composition of alloys has been tuned by changing the growth temperatures. As a result, we can tune the bandgap which varies from 1.73 eV to 1.84 eV. The detailed theoretical calculation supports the experimental observation and shows a possibility of wide tunability of bandgap.
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Submitted 2 May, 2017;
originally announced May 2017.
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Integral Inequalities in Thermodynamics
Authors:
Anuj S. Apte
Abstract:
Thermodynamic systems involving reversible and non-reversible heat transfer are used to derive integral inequalities expected from the Second of Law of Thermodynamics. Then, the inequalities are proved and generalized to higher dimensions with intended application of being used as a quick way of generating numerous other inequalities such as the Weighted Means Inequality. The proofs also serve as…
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Thermodynamic systems involving reversible and non-reversible heat transfer are used to derive integral inequalities expected from the Second of Law of Thermodynamics. Then, the inequalities are proved and generalized to higher dimensions with intended application of being used as a quick way of generating numerous other inequalities such as the Weighted Means Inequality. The proofs also serve as a way of establishing the equivalence of the Planck's statement of the Second Law and the positivity of specific heats.
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Submitted 28 December, 2018; v1 submitted 14 February, 2016;
originally announced February 2016.
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The freezing tendency towards 4-coordinated amorphous network causes increase in heat capacity of supercooled Stillinger-Weber silicon
Authors:
Pankaj A. Apte,
Nandlal Pingua,
Arvind Kumar Gautam,
Uday Kumar,
Soohaeng Yoo Willow,
Xiao Cheng Zeng,
B. D. Kulkarni
Abstract:
The supercooled liquid silicon, modeled by Stillinger-Weber potential, shows anomalous increase in heat capacity $C_p$, with a maximum $C_p$ value close to 1060 K at zero pressure. We study equilibration and relaxation of the supercooled SW Si, in the temperature range of 1060 K--1070 K at zero pressure. We find that as the relaxation of the metastable supercooled liquid phase initiates, a straigh…
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The supercooled liquid silicon, modeled by Stillinger-Weber potential, shows anomalous increase in heat capacity $C_p$, with a maximum $C_p$ value close to 1060 K at zero pressure. We study equilibration and relaxation of the supercooled SW Si, in the temperature range of 1060 K--1070 K at zero pressure. We find that as the relaxation of the metastable supercooled liquid phase initiates, a straight line region (SLR) is formed in cumulative potential energy distributions. The configurational temperature corresponding to the SLR is close to 1060 K, which was earlier identified as the freezing temperature of 4-coordinated amorphous network. The SLR is found to be tangential to the distribution of the metastable liquid phase and thus influences the broadness of the distribution. As the bath temperature is reduced from 1070 K to 1060 K, the effective temperature approaches the bath temperature which results in broadening of the metastable phase distribution. This, in turn, causes an increase in overall fluctuations of potential energy and hence an increase of heat capacity. We also find that during initial stages of relaxation, 4-coordinated atoms form 6-membered rings with a chair--like structure and other structural units that indicate crystallization. Simultaneously a strong correlation is established between the number of chair-shaped 6-membered rings and the number of 4-coordinated atoms in the system. This shows that all properties related to 4-coordinated particles are highly correlated as the SLR is formed in potential energy distributions and this can be interpreted as a consequence of `freezing' of amorphous network formed by 4-coordinated particles.
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Submitted 10 April, 2014;
originally announced April 2014.
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Nonmonotonic dependence of the absolute entropy on temperature in supercooled Stillinger-Weber silicon
Authors:
Pankaj A. Apte,
Arvind K. Gautam
Abstract:
Using a recently developed thermodynamic integration method, we compute the precise values of the excess Gibbs free energy (G^e) of the high density liquid (HDL) phase with respect to the crystalline phase at different temperatures (T) in the supercooled region of the Stillinger-Weber (SW) silicon [F. H. Stillinger and T. A. Weber, Phys. Rev. B. 32, 5262 (1985)]. Based on the slope of G^e with res…
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Using a recently developed thermodynamic integration method, we compute the precise values of the excess Gibbs free energy (G^e) of the high density liquid (HDL) phase with respect to the crystalline phase at different temperatures (T) in the supercooled region of the Stillinger-Weber (SW) silicon [F. H. Stillinger and T. A. Weber, Phys. Rev. B. 32, 5262 (1985)]. Based on the slope of G^e with respect to T, we find that the absolute entropy of the HDL phase increases as its enthalpy changes from the equilibrium value at T \ge 1065 K to the value corresponding to a non-equilibrium state at 1060 K. We find that the volume distribution in the equilibrium HDL phases become progressively broader as the temperature is reduced to 1060 K, exhibiting van-der-Waals (VDW) loop in the pressure-volume curves. Our results provides insight into the thermodynamic cause of the transition from the HDL phase to the low density phases in SW silicon, observed in earlier studies near 1060 K at zero pressure.
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Submitted 3 October, 2012; v1 submitted 15 August, 2011;
originally announced August 2011.
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Evidence for coincidence of Kauzmann temperature and liquid-liquid transition temperature in supercooled silicon
Authors:
Pankaj A. Apte,
Arvind K. Gautam,
Amol M. Patil
Abstract:
The paper is withdrawn.
The paper is withdrawn.
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Submitted 29 August, 2011; v1 submitted 1 October, 2010;
originally announced October 2010.
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Efficient computation of free energy of crystal phases due to external potentials by error-biased Bennett acceptance ratio method
Authors:
Pankaj A. Apte
Abstract:
Free energy of crystal phases is commonly evaluated by thermodynamic integration (TDI) along a reversible path that involves an external potential. A persistent problem in this method is that a significant hysteresis is observed due to differences in the center of mass position of the crystal phase in the presence and absence of the external potential. To alleviate this hysteresis, a constraint…
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Free energy of crystal phases is commonly evaluated by thermodynamic integration (TDI) along a reversible path that involves an external potential. A persistent problem in this method is that a significant hysteresis is observed due to differences in the center of mass position of the crystal phase in the presence and absence of the external potential. To alleviate this hysteresis, a constraint on the translational degrees of freedom of the crystal phase is imposed along the path and subsequently a correction term is added to the free energy to account for such a constraint. In this work, we propose a new methodology termed as error-biased Bennett Acceptance ratio (EBAR) method that effectively solves this problem without the need to impose any constraint. This method is simple to implement as it does not require any modification to the path or to the simulation code. We show the applicability of this method in the computation of crystal-melt interfacial energy by cleaving wall method [J. Chem. Phys., 118, 7651 (2003)] and bulk crystal-melt free energy difference by constrained fluid $λ$-integration method [J. Chem. Phys., 120, 2122 (2004)] for a model potential of silicon.
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Submitted 1 December, 2009; v1 submitted 21 June, 2009;
originally announced June 2009.