Generalized eigenstate typicality in translation-invariant quasifree fermionic models

TL;DR

This paper extends the concept of eigenstate thermalization to translation-invariant quasifree fermionic models, showing most eigenstates with certain constraints resemble generalized Gibbs ensembles locally, supported by analytical and numerical evidence.

Contribution

It introduces a generalized eigenstate thermalization framework for quasifree fermionic models, broadening understanding of thermalization in quantum systems.

Findings

Most eigenstates with fixed constraints approximate generalized Gibbs ensembles.

Analytical results are generalized from previous work by Lai and Yang.

Numerical illustrations are provided using the Jordan-Wigner transform of the XX spin chain.

Abstract

We demonstrate a generalized notion of eigenstate thermalization for translation-invariant quasifree fermionic models: the vast majority of eigenstates satisfying a finite number of suitable constraints (e.g. fixed energy and particle number) have the property that their reduced density matrix on small subsystems approximates the corresponding generalized Gibbs ensemble. To this end, we generalize analytic results by Lai and Yang (Phys. Rev. B 91, 081110 (2015)) and illustrate the claim numerically by example of the Jordan-Wigner transform of the XX spin chain.