Thermalization Dynamics in Closed Quantum Many Body Systems: a Precision Large Scale Exact Diagonalization Study

TL;DR

This study uses large-scale exact diagonalization to analyze thermalization in closed quantum many-body systems, revealing how local observables relax and how entropy and deviations from thermal states scale with system size and energy.

Contribution

It provides a detailed, high-precision analysis of thermalization dynamics in non-integrable quantum spin systems using advanced numerical methods.

Findings

Deviations from thermal states are well described by the eigenstate thermalization hypothesis.

Von Neumann entropy correction scales with the square of local operator scaling.

Local observables relax exponentially with a system-size-dependent time scale.

Abstract

Using a Krylov-subspace time evolution algorithm, we simulate the real-time dynamics of translation invariant non-integrable finite spin rings to quite long times with high accuracy. We systematically study the finite-size deviation between the resulting equilibrium state and the thermal state, and we highlight the importance of the energy variance on the deviations. We find that the deviations are well described by the eigenstate thermalization hypothesis, and that the von Neumann entropy correction scaling is the square of the local operator scaling. We reveal also an area law contribution to the relaxed von Neumann entropy, which we connect to the mutual information between the considered subsystem and its immediate environment. We also find that local observables relax towards equilibrium exponentially with a relaxation time scale that grows linearly with system length and is somewhat independent of the local operator, but depends strongly on the energy of the initial state, with the fastest relaxation times found towards one end of the overall energy spectrum. To contrast this behaviour we also study domain wall initial states, which exhibit clear diffusive behaviour, with a Thouless time scaling quadratically with the systems size, leading to a rather precise estimate for the diffusion constant for states in the vicinity of the middle of the energy spectrum.