Eigenstate Thermalization Hypothesis and Free Probability
arXiv:2204.11679 · doi:10.1103/PhysRevLett.129.170603
Abstract
Quantum thermalization is well understood via the Eigenstate Thermalization Hypothesis (ETH). The general form of ETH, describing all the relevant correlations of matrix elements, may be derived on the basis of a `typicality' argument of invariance with respect to local rotations involving nearby energy levels. In this work, we uncover the close relation between this perspective on ETH and Free Probability theory, as applied to a thermal ensemble or an energy shell. This mathematical framework allows one to reduce in a straightforward way higher-order correlation functions to a decomposition given by minimal blocks, identified as free cumulants, for which we give an explicit formula. This perspective naturally incorporates the consistency property that local functions of ETH operators also satisfy ETH. The present results uncover a direct connection between the Eigenstate Thermalization Hypothesis and the structure of Free Probability, widening considerably the latter's scope and highlighting its relevance to quantum thermalization.
arXiv comment5 pages, 2 figures and 5 pages of supplementary material. This paper has been submitted simultaneously with "Dynamics of Fluctuations in the Open Quantum SSEP and Free Probability" by L. Hruza and D. Bernard, which discusses the appearance of free cumulants in stochastic a transport model
References in corpus (38)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Nonequilibrium dynamics of closed interacting quantum systems
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- A bound on chaos
- Chaos in quantum channels
- Canonical Typicality
- The approach to thermal equilibrium in quantized chaotic systems
- A Universal Operator Growth Hypothesis
- Cleaning large correlation matrices: tools from random matrix theory
- Thermal Fluctuations in Quantized Chaotic Systems
- Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
- Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
- The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators
- Quantum chaos and thermalization in gapped systems
- Bounds on chaos from the eigenstate thermalization hypothesis
- Typical fast thermalization processes in closed many-body systems
- Fluctuation-Dissipation Theorem in an Isolated System of Quantum Dipolar Bosons after a Quench
- Normal Typicality and von Neumann's Quantum Ergodic Theorem
- Canonical thermalization
- Euclidean operator growth and quantum chaos
- Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies
- Structure of chaotic eigenstates and their entanglement entropy
- Eigenstate Correlations, Thermalization and the Butterfly Effect
- A two-way approach to out-of-time-order correlators
- Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
- A statistical mechanism for operator growth
- Out-of-time-order correlations and the fine structure of eigenstate thermalisation
- Multipartite entanglement structure in the Eigenstate Thermalization Hypothesis
- Bound on the exponential growth rate of out-of-time-ordered correlators
- High-temperature Expansions and Message Passing Algorithms
- Degenerate observables and the many Eigenstate Thermalization Hypotheses
- Quantum bounds and fluctuation-dissipation relations
- Universal fluctuations around typicality for quantum ergodic systems
- Many-body systems with random spatially local interactions
- The combinatorics of Green's functions in planar field theories
- Hamiltonian Dynamics of a Sum of Interacting Random Matrices
- Equilibration of quantum cat states
Cited by in corpus (54)
- Many-Body Localization in the Age of Classical Computing
- Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
- Purification Timescales in Monitored Fermions
- Noncommuting conserved charges in quantum thermodynamics and beyond
- A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity
- Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
- Deep thermalization in constrained quantum systems
- Full Eigenstate Thermalization via Free Cumulants in Quantum Lattice Systems
- Interactions and integrability in weakly monitored Hamiltonian systems
- Multiboundary wormholes and OPE statistics
- Magic Resources of the Heisenberg Picture
- Entanglement Growth and Minimal Membranes in Random Unitary Circuits
- Hilbert space delocalization under random unitary circuits
- Non-Hermitian Hamiltonians Violate the Eigenstate Thermalization Hypothesis
- Catching thermal avalanches in the disordered XXZ model
- Hydrodynamics and the eigenstate thermalization hypothesis
- Quantum bounds on the generalized Lyapunov exponents
- Designs via Free Probability
- Eigenstate correlations, the eigenstate thermalization hypothesis, and quantum information dynamics in chaotic many-body quantum systems
- Microcanonical windows on quantum operators
- Normal weak eigenstate thermalization
- Anticoncentration and state design of random tensor networks
- Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems
- Generalized Free Cumulants for Quantum Chaotic Systems
- Bernoulli variables, classical exclusion processes and free probability
- Exact Entanglement in the Driven Quantum Symmetric Simple Exclusion Process
- Nonstabilizerness dynamics in many-body localized systems
- Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems
- Quantum master equation from the eigenstate thermalization hypothesis
- Microcanonical Free Cumulants in lattice systems
- Many-body localization crossover is sharper in quasiperiodic spin chains
- Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits
- Fermionic Magic Resources of Quantum Many-Body Systems
- Large Deviations in Switching Diffusion: from Free Cumulants to Dynamical Transitions
- Exceptional stationary state in a dephasing many-body open quantum system
- Subsystem entropy in 2d CFT and KdV ETH
- Random matrix universality in dynamical correlation functions at late times
- Typical thermalization of low-entanglement states
- A Strategy for Proving the Strong Eigenstate Thermalization Hypothesis : Chaotic Systems and Holography
- Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
- Emergent random matrix universality in quantum operator dynamics
- Late-time ensembles of quantum states in quantum chaotic systems
- Entanglement dynamics and eigenstate correlations in strongly disordered quantum many-body systems
- Out-of-equilibrium Eigenstate Thermalization Hypothesis
- Probes of Full Eigenstate Thermalization in Ergodicity-Breaking Quantum Circuits
- Quantum Thermalization via Travelling Waves
- Structured random matrices and cyclic cumulants: A free probability approach
- Numerical evidence for the non-Abelian eigenstate thermalization hypothesis
- Emergent Thermalization Thresholds in Unitary Dynamics of Inhomogeneously Disordered Quantum Systems
- On a Matrix Ensemble for Arbitrary Complex Quantum Systems
- Transport in a System with a Tower of Quantum Many-Body Scars
- A universal sum over topologies in 3d gravity
- Eigenstate Thermalization Hypothesis and Random Matrix Theory Universality in Few-Body Systems
- Diagrammatics of free energies with fixed variance for high-dimensional data