Identifying the closeness of eigenstates in quantum many-body systems

TL;DR

This paper introduces modulus fidelity as a new measure to quantify the closeness of eigenstates in quantum many-body systems, revealing differences between integrable and non-integrable regimes and linking eigenstate closeness to thermalization.

Contribution

It proposes modulus fidelity for analyzing eigenstate closeness and demonstrates its effectiveness in distinguishing integrable and non-integrable systems, connecting eigenstate properties to ETH.

Findings

Modulus fidelity fluctuates in integrable systems and stabilizes in non-integrable systems.

Average modulus fidelity increases with parameters that induce chaos.

Eigenstates with small level spacing are closer in non-integrable systems.

Abstract

We propose a new quantity called modulus fidelity to measure the closeness of two quantum pure states. Especially, we use it to investigate the closeness of eigenstates of quantum many-body systems. When the system is integrable, the modulus fidelity of neighbor eigenstates displays a large fluctuation. But the modulus fidelity is close to a constant when system becomes non-integrable with fluctuation reduced drastically. Average modulus fidelity of neighbor eigenstates increases with the increase of parameters that destroy the integrability, which also indicates the integrable-chaos transition. In non-integrable case, it is found two eigenstates are closer to each other if their level spacing is small. We also show that the closeness of eigenstates in non-integrable domain is the underlying mechanism of \emph{eigenstate thermalization hypothesis} (ETH) which explains the thermalization in nonintegrable system we studied.