In a free fermion chain, the coarse-grained density distribution becomes almost uniform at sufficiently large typical times for any initial state with fixed macroscopic particle number, proving macroscopic irreversibility from unitary evolution.
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From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
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This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of ideas from quantum chaos and random matrix theory (RMT). To this end, we present a brief overview of classical and quantum chaos, as well as RMT and some of its most important predictions. The latter include the statistics of energy levels, eigenstate components, and matrix elements of observables. Building on these, we introduce the ETH and show that it allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath. We examine numerical evidence of eigenstate thermalization from studies of many-body lattice systems. We also introduce the concept of a quench as a means of taking isolated systems out of equilibrium, and discuss results of numerical experiments on quantum quenches. The second part of the review explores the implications of quantum chaos and ETH to thermodynamics. Basic thermodynamic relations are derived, including the second law of thermodynamics, the fundamental thermodynamic relation, fluctuation theorems, and the Einstein and Onsager relations. In particular, it is shown that quantum chaos allows one to prove these relations for individual Hamiltonian eigenstates and thus extend them to arbitrary stationary statistical ensembles. We then show how one can use these relations to obtain nontrivial universal energy distributions in continuously driven systems. At the end of the review, we briefly discuss the relaxation dynamics and description after relaxation of integrable quantum systems, for which ETH is violated. We introduce the concept of the generalized Gibbs ensemble, and discuss its connection with ideas of prethermalization in weakly interacting systems.
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Introduces a local one-point fidelity correlator to define SW-SSB, preserving key features like channel stability and long-range conditional mutual information while enabling detection in large and thermodynamic-limit systems.
Exact modular S-transforms are derived for GGEs in the symplectic fermion theory, agreeing with conjectures for the W3 zero mode and mirroring free-fermion results for the KdV subset.
Retarded correlators of bulk scalars and Wilson-line displacement operators exhibit bouncing singularities at t_c=β/2(1+i) with matching WKB and asymptotic OPE data, implying a universal high-frequency factorization.
Rigorous proof that random half-chain initial states in a low-density free-fermion model thermalize, with local particle counts matching equilibrium at long times with high probability.
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
CoMPuTE replaces von Neumann entropy with Rényi-2 purity in the LITE algorithm, enabling faster and more stable late-time simulations of quantum transport.
The quantum cubic Szegő equation exhibits integer spectra for its Hamiltonian and conserved hierarchies, indicating superintegrability beyond ordinary quantum integrability.
Typical states in large-N holographic CFTs exhibit UV and IR length scales set by energy and charges, producing factorization that isolates black holes via a corona of saturated entanglement wedges and extends ETH to rotating ensembles.
Fock space cages from destructive interference in kinetically constrained models yield localized many-body eigenstates and non-ergodic dynamics by treating Fock space as a graph of bitstring states.
The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
Randomizing Fock-space connections in the quantum East model preserves the localization transition, showing that Fock-space graph structure matters more than geometric locality.
An emergent gauge symmetry valid only in a subset of sectors of the fragmented S=1 dipole-conserving spin chain enables exact quantum simulation of gauge theories using a non-gauge-invariant Hamiltonian.
Provides two sets of conditions on GQCAs guaranteeing thermalization to infinite temperature via a quantum many-body generalization of the Riemann-Lebesgue lemma for states with bounded density.
Key equilibrium distributions and entropies of statistical mechanics emerge from quantum envariance and exchange symmetry in system-environment entangled states.
Numerical study of a qutrit lattice with conserved charge shows thermalization signatures in states outside microcanonical windows of energy and charge, supporting a generalized form of ETH called generic ETH.
In a driven non-integrable Ising chain, subsystem reduced density matrices and work statistics both detect the frequency-dependent crossover from prethermal to infinite-temperature Floquet regimes.
The paper organizes important open questions in quantum gravity and quantum information into four themes without presenting new results or derivations.
A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.
citing papers explorer
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Macroscopic Irreversibility in Quantum Systems: Free Expansion in a Fermion Chain
In a free fermion chain, the coarse-grained density distribution becomes almost uniform at sufficiently large typical times for any initial state with fixed macroscopic particle number, proving macroscopic irreversibility from unitary evolution.
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Local Strong-to-Weak Spontaneous Symmetry Breaking
Introduces a local one-point fidelity correlator to define SW-SSB, preserving key features like channel stability and long-range conditional mutual information while enabling detection in large and thermodynamic-limit systems.
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Modular Properties of Symplectic Fermion Generalised Gibbs Ensemble
Exact modular S-transforms are derived for GGEs in the symplectic fermion theory, agreeing with conjectures for the W3 zero mode and mirroring free-fermion results for the KdV subset.
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Bouncing singularities and thermal correlators on line defects
Retarded correlators of bulk scalars and Wilson-line displacement operators exhibit bouncing singularities at t_c=β/2(1+i) with matching WKB and asymptotic OPE data, implying a universal high-frequency factorization.
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Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system
Rigorous proof that random half-chain initial states in a low-density free-fermion model thermalize, with local particle counts matching equilibrium at long times with high probability.
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Hilbert Space Fragmentation from Generalized Symmetries
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
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Compressed minimum-purity time evolution for late-time quantum dynamics
CoMPuTE replaces von Neumann entropy with Rényi-2 purity in the LITE algorithm, enabling faster and more stable late-time simulations of quantum transport.
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A superintegrable quantum field theory
The quantum cubic Szegő equation exhibits integer spectra for its Hamiltonian and conserved hierarchies, indicating superintegrability beyond ordinary quantum integrability.
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Entanglement inequalities, black holes and the architecture of typical states
Typical states in large-N holographic CFTs exhibit UV and IR length scales set by energy and charges, producing factorization that isolates black holes via a corona of saturated entanglement wedges and extends ETH to rotating ensembles.
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Localized Fock Space Cages in Kinetically Constrained Models
Fock space cages from destructive interference in kinetically constrained models yield localized many-body eigenstates and non-ergodic dynamics by treating Fock space as a graph of bitstring states.
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The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities
The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
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Locality versus Fock-space structure in East-type models
Randomizing Fock-space connections in the quantum East model preserves the localization transition, showing that Fock-space graph structure matters more than geometric locality.
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Hilbert Space Fragmentation and Gauge Symmetry
An emergent gauge symmetry valid only in a subset of sectors of the fragmented S=1 dipole-conserving spin chain enables exact quantum simulation of gauge theories using a non-gauge-invariant Hamiltonian.
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Thermalization with Gaussian Quantum Cellular Automata
Provides two sets of conditions on GQCAs guaranteeing thermalization to infinite temperature via a quantum many-body generalization of the Riemann-Lebesgue lemma for states with bounded density.
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Statistical mechanics from quantum envariance and exchange symmetry
Key equilibrium distributions and entropies of statistical mechanics emerge from quantum envariance and exchange symmetry in system-environment entangled states.
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Generic ETH: Eigenstate Thermalization beyond the Microcanonical
Numerical study of a qutrit lattice with conserved charge shows thermalization signatures in states outside microcanonical windows of energy and charge, supporting a generalized form of ETH called generic ETH.
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Subsystem Thermalization and Work Statistical Characterizations of Floquet Dynamics
In a driven non-integrable Ising chain, subsystem reduced density matrices and work statistics both detect the frequency-dependent crossover from prethermal to infinite-temperature Floquet regimes.
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Rethinking quantum information in gravity and fields
The paper organizes important open questions in quantum gravity and quantum information into four themes without presenting new results or derivations.
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Coherent and dissipative dynamics at quantum phase transitions
A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.