Thermalization of Interacting Fermions and Delocalization in Fock space

TL;DR

This paper investigates how increasing interactions in 1D fermionic systems lead to eigenstate thermalization and ergodicity, showing that fluctuations decrease with system size and coupling, indicating delocalization in Fock space.

Contribution

It demonstrates the relationship between eigenstate fluctuations, participation ratio, and the onset of thermalization in interacting fermions using exact diagonalization.

Findings

Fluctuations decrease with system size and interaction strength

Eigenstate thermalization occurs even for small perturbations in large systems

Fluctuations are proportional to the inverse participation ratio

Abstract

By means of exact diagonalization, we investigate the onset of 'eigenstate thermalization' and the crossover to ergodicity in a system of 1D fermions with increasing interaction. We show that the fluctuations in the expectation values of the momentum distribution from eigenstate to eigenstate decrease with increasing coupling strength and system size. It turns out that these fluctuations are proportional to the inverse participation ratio of eigenstates represented in the Fock basis. We demonstrate that eigenstate thermalization should set in even for vanishingly small perturbations in the thermodynamic limit.