Non-Abelian eigenstate thermalization hypothesis
arXiv:2206.05310 · doi:10.1103/PhysRevLett.130.140402
Abstract
The eigenstate thermalization hypothesis (ETH) explains why chaotic quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity ("charge"), the ETH implies thermalization within a charge sector -- in a microcanonical subspace. But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist. Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local observables' time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we also find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics.
arXiv comment5 pages (+Supplementary Material: 11 pages). Final version published in Physical Review Letters
References in corpus (53)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Generalized Gibbs ensemble in integrable lattice models
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- Experimental Observation of a Generalized Gibbs Ensemble
- Eigenstate Thermalization Hypothesis
- The approach to thermal equilibrium in quantized chaotic systems
- Breakdown of thermalization in finite one-dimensional systems
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
- Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
- Ultracold atoms out of equilibrium
- Does a single eigenstate encode the full Hamiltonian?
- Thermal Fluctuations in Quantized Chaotic Systems
- The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators
- Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
- Thermodynamics of quantum systems with multiple conserved quantities
- Bounds on chaos from the eigenstate thermalization hypothesis
- On Conservation Laws, Relaxation and Pre-relaxation after a Quantum Quench
- Thermodynamic resource theories, non-commutativity and maximum entropy principles
- Eigenstate thermalization and quantum chaos in the Holstein polaron model
- The isolated Heisenberg magnet as a quantum time crystal
- Thermodynamic length in open quantum systems
- Renyi Entropy of Chaotic Eigenstates
- Structure of chaotic eigenstates and their entanglement entropy
- Information erasure without an energy cost
- The squeezed thermal reservoir as a generalized equilibrium reservoir
- Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
- Thermodynamics as a Consequence of Information Conservation
- Thermalization of Gauge Theories from their Entanglement Spectrum
- Noncommuting conserved quantities in quantum many-body thermalization
- Hybrid Thermal Machines: Generalized Thermodynamic Resources for Multitasking
- Beyond heat baths II: Framework for generalized thermodynamic resource theories
- Non-Abelian symmetry can increase entanglement entropy
- Non-Abelian Quantum Transport and Thermosqueezing Effects
- Stationary State Degeneracy of Open Quantum Systems with Non-Abelian Symmetries
- The eigenstate thermalization hypothesis in constrained Hilbert spaces: a case study in non-Abelian anyon chains
- On the local equivalence between the canonical and the microcanonical distributions for quantum spin systems
- The first law of general quantum resource theories
- An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains
- Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond i.i.d. scaling
- Quantum heat engine operating between thermal and spin reservoirs
- Quantum Reference Frames and Their Applications to Thermodynamics
- How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics
- Reference frames which separately store non-commuting conserved quantities
- Revealing missing charges with generalised quantum fluctuation relations
- Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems
- Characterizing symmetry-protected thermal equilibrium by work extraction
- Eigenstate Thermalization Hypothesis and Approximate Quantum Error Correction
- Fluctuations of work in realistic equilibrium states of quantum systems with conserved quantities
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- SU(2) Gauge Theory in Dimensions on a Plaquette Chain Obeys the Eigenstate Thermalization Hypothesis
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- Quantum Computing Universal Thermalization Dynamics in a (2+1)D Lattice Gauge Theory
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- Unveiling Eigenstate Thermalization for Non-Hermitian systems
- Noncommuting charges can remove non-stationary quantum many-body dynamics
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- A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
- Eigenstate thermalization in spin- systems with SU(2) symmetry
- Imperfect Many-Body Localization in Exchange-Disordered Isotropic Spin Chains
- General theory for discrete symmetry-breaking equilibrium states
- Engineering Hierarchical Symmetries
- No-Signaling in Steepest Entropy Ascent: A Nonlinear Non-local Non-equilibrium Quantum Dynamics of Composite Systems
- Automated detection of symmetry-protected subspaces in quantum simulations
- Entanglement patterns of quantum chaotic Hamiltonians with a scalar U(1) charge
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- Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions
- Numerical evidence for the non-Abelian eigenstate thermalization hypothesis
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- Thermalization of Quantum Many-Body Scars in Kinetically Constrained Systems
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- Subsystem Thermalization Hypothesis in Quantum Spin Chains with Conserved Charges
- Trade-off between diagonal and off-diagonal elements in the eigenstate thermalization hypothesis
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