Full Eigenstate Thermalization via Free Cumulants in Quantum Lattice Systems
arXiv:2303.00713 · doi:10.1103/PhysRevLett.134.140404
Abstract
The Eigenstate-Thermalization-Hypothesis (ETH) has been established as the general framework to understand quantum statistical mechanics. Only recently has the attention been paid to so-called full ETH, which accounts for higher-order correlations among matrix elements, and that can be rationalized theoretically using the language of Free Probability. In this work, we perform the first numerical investigation of the full ETH in physical many-body systems with local interactions by testing the decomposition of higher-order correlators into thermal free cumulants for local operators. We perform exact diagonalization on two classes of local non-integrable (chaotic) quantum many-body systems: spin chain Hamiltonians and Floquet brickwork unitary circuits. We show that the dynamics of four-time correlation functions are encoded in fourth-order free cumulants, as predicted by ETH. Their dependence on frequency encodes the physical properties of local many-body systems and distinguishes them from structureless, rotationally invariant ensembles of random matrices.
arXiv comment5 pages, 3 figures + Supplementary Material. v3: added an introduction to Free Cumulants in the Supp. Mat
References in corpus (48)
- 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
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- The approach to thermal equilibrium in quantized chaotic systems
- Chaos and complexity by design
- Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
- Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
- Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
- Anomalous thermalization in ergodic systems
- Introduction to Random Matrices - Theory and Practice
- Off-diagonal matrix elements of local operators in many-body quantum systems
- Eigenstate thermalization within isolated spin-chain systems
- Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
- The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators
- Entanglement and matrix elements of observables in interacting integrable systems
- Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
- Bounds on chaos from the eigenstate thermalization hypothesis
- Eigenstate Thermalization in a Locally Perturbed Integrable System
- Long tail distributions near the many body localization transition
- Ergodic properties of a generic non-integrable quantum many-body system in thermodynamic limit
- Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis in a One-Dimensional Interacting Bose gas
- Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
- Exact emergent quantum state designs from quantum chaotic dynamics
- Maximum velocity quantum circuits
- Eigenstate thermalization in the Sachdev-Ye-Kitaev model
- Eigenstate Thermalization Hypothesis and Free Probability
- Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies
- Local pairing of Feynman histories in many-body Floquet models
- Fluctuations in ballistic transport from Euler hydrodynamics
- Eigenstate Correlations, Thermalization and the Butterfly Effect
- Transport fluctuations in integrable models out of equilibrium
- Solvable model of deep thermalization with distinct design times
- Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
- Second Order Freeness and Fluctuations of Random Matrices, III. Higher order freeness and free cumulants
- Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
- Bound on Eigenstate Thermalization from Transport
- Out-of-time-order correlations and the fine structure of eigenstate thermalisation
- Generalized Deep Thermalization for Free Fermions
- Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
- Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems
- High-temperature Expansions and Message Passing Algorithms
- Eigenstate thermalization and rotational invariance in ergodic quantum systems
- Spectral decoupling in many-body quantum chaos
- Exact Universal Chaos, Speed Limit, Acceleration, Planckian Transport Coefficient, "Collapse" to equilibrium, and Other Bounds in Thermal Quantum Systems
- Microcanonical Free Cumulants in lattice systems
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- Exactly solvable many-body dynamics from space-time duality
- Nonstabilizerness dynamics in many-body localized systems
- Quantum master equation from the eigenstate thermalization hypothesis
- Fermionic Magic Resources of Quantum Many-Body Systems
- Random matrix universality in dynamical correlation functions at late times
- Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
- Late-time ensembles of quantum states in quantum chaotic systems
- Emergent random matrix universality in quantum operator dynamics
- Out-of-equilibrium Eigenstate Thermalization Hypothesis
- Probes of Full Eigenstate Thermalization in Ergodicity-Breaking Quantum Circuits
- Statistics of the Random Matrix Spectral Form Factor
- Complexity of Quadratic Quantum Chaos
- Transport in a System with a Tower of Quantum Many-Body Scars
- Emergent Thermalization Thresholds in Unitary Dynamics of Inhomogeneously Disordered Quantum Systems
- Eigenstate Thermalization Hypothesis and Random Matrix Theory Universality in Few-Body Systems