The approach to typicality in many-body quantum systems

TL;DR

This paper provides numerical evidence that many-body lattice systems tend to exhibit typical thermal behavior as the number of subsystems increases, supporting the eigenstate thermalization hypothesis and revealing how deviations decrease with system size.

Contribution

It demonstrates that many-body lattice systems approach typicality with increasing subsystems and characterizes the atypicality decay, extending understanding of thermalization in quantum systems.

Findings

Deviations from typicality decrease exponentially with the number of subsystems.

Averaging over random interactions yields a power-law decay of atypicality.

Results support the eigenstate thermalization hypothesis in many-body systems.

Abstract

The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization. Here we give numerical evidence that many-body lattice systems generically approach typicality as the number of subsystems is increased, and thus provide further support for the eigenstate thermalization hypothesis. Our results indicate that the deviation of many-body systems from typicality decreases exponentially with the number of systems. Further, by averaging over a number of randomly-selected nearest-neighbor interactions, we obtain a power-law for the atypicality as a function of the Hilbert space dimension, distinct from the power-law possessed by random Hamiltonians.