Localized Thermal States

TL;DR

This paper challenges the common belief that thermalization requires fully delocalized eigenstates, showing that in systems with two-body interactions, localized eigenstates can also exhibit thermal properties under certain conditions.

Contribution

It introduces a semi-analytical approach to identify conditions where localized eigenstates in interacting boson systems behave thermally, supported by numerical validation.

Findings

Localized thermal eigenstates exist in systems with two-body interactions.

The semi-analytical model accurately predicts conditions for thermalization.

Numerical data confirms the presence of localized thermal states.

Abstract

It is believed that thermalization in closed systems of interacting particles can occur only when the eigenstates are fully delocalized and chaotic in the preferential (unperturbed) basis of the total Hamiltonian. Here we demonstrate that at variance with this common belief the typical situation in the systems with two-body inter-particle interaction is much more complicated and allows to treat as thermal even eigenstates that are not fully delocalized. Using a semi-analytical approach we establish the conditions for the emergence of such thermal states in a model of randomly interacting bosons. Our numerical data show an excellent correspondence with the predicted properties of {\it localized thermal eigenstates}.