Two-particle self-consistency in a system without condensation

TL;DR

This paper explores two-particle self-consistency in non-condensing systems, analyzing correlations and conservation laws to understand thermalization and eigenstate properties in complex quantum systems.

Contribution

It introduces a new perspective on local conservation and correlations in nonintegrable systems, advancing the understanding of two-particle self-consistency without condensation.

Findings

Analysis of correlations between decompositions of four-point functions

Identification of local conservation laws in nonintegrable systems

Insights into the relationship between self-energy and Green functions

Abstract

In a generic random system, the coexistence of extended and localized states can be evidenced by the subextensive width of energy distribution of a physical initial state in, for example, the quantum quenches which involving the local Hamiltonian. The robust thermalization is also evidenced in terms of the microscopic canonical ensemble average in the thermalization limit\cite{Shiraishi}, which satisfies the weak eigenstate thermalization hypothesis (ETH). In this article, we study the method of two-particle self-consistency for a system without condensation, i.e., without the inaccessible localizations that violating the ETH. We provide another pespective that considering the local conservation of an nonintegrable system the stubborn correlations between the three kinds of decompositions for the four-point functions, which can be regarded as the elements in a product of the self-energy and Green function matrices (i.e., the two-particle correlations in Kadanoff and Baym notation\cite{Vilk Y M}).