Eigenstate correlations, the eigenstate thermalization hypothesis, and quantum information dynamics in chaotic many-body quantum systems

Abstract

We consider the statistical properties of eigenstates of the time-evolution operator in chaotic many-body quantum systems. Our focus is on correlations between eigenstates that are specific to spatially extended systems and that characterise entanglement dynamics and operator spreading. In order to isolate these aspects of dynamics from those arising as a result of local conservation laws, we consider Floquet systems in which there are no conserved densities. The correlations associated with scrambling of quantum information lie outside the standard framework established by the eigenstate thermalisation hypothesis (ETH). In particular, ETH provides a statistical description of matrix elements of local operators between pairs of eigenstates, whereas the aspects of dynamics we are concerned with arise from correlations amongst sets of four or more eigenstates. We establish the simplest correlation function that captures these correlations and discuss features of its behaviour that are expected to be universal at long distances and low energies. We also propose a maximum-entropy Ansatz for the joint distribution of a small number $n$ of eigenstates. In the case $n=2$ this Ansatz reproduces ETH. For $n=4$ it captures both the growth with time of entanglement between subsystems, as characterised by the purity of the time-evolution operator, and also operator spreading, as characterised by the behaviour of the out-of-time-order correlator. We test these ideas by comparing results from Monte Carlo sampling of our Ansatz with exact diagonalisation studies of Floquet quantum circuits.

arXiv comment25 pages, 24 figures

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Cited by in corpus (9)

• A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity
• Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
• Entanglement dynamics and eigenstate correlations in strongly disordered quantum many-body systems
• Probes of Full Eigenstate Thermalization in Ergodicity-Breaking Quantum Circuits
• Logarithmic entanglement lightcone from eigenstate correlations in the many-body localised phase
• Out-of-equilibrium Eigenstate Thermalization Hypothesis
• Emergent Thermalization Thresholds in Unitary Dynamics of Inhomogeneously Disordered Quantum Systems
• Temporal Entanglement Transitions in the Periodically Driven Ising Chain