Observable-manifested correlations in many-body quantum chaotic systems

TL;DR

This paper explores how observable correlations in many-body quantum chaotic systems differ from random models, revealing the role of eigenstate structures and correlations in shaping observable properties and deviations from random matrix theory.

Contribution

It uncovers the significance of eigenstate correlations in realistic quantum chaotic systems and explains deviations from random matrix theory predictions through numerical analysis.

Findings

Off-diagonal observable elements decay exponentially in realistic systems

Correlations in eigenstates influence the structure of observable envelope functions

Deviations from RMT are explained by Hamiltonian-induced correlations

Abstract

In this paper, we investigate the distinctions between realistic quantum chaotic systems and random models from the perspective of observable properties, particularly focusing on the eigenstate thermalization hypothesis (ETH). Through numerical simulations, we find that for realistic systems, the envelope function of off-diagonal elements of observables exhibits an exponential decay at large $\Delta E$, while for randomized models, it tends to be flat. We demonstrate that the correlations of chaotic eigenstates, originating from the delicate structures of Hamiltonians, play a crucial role in the non-trivial structure of the envelope function. Furthermore, we analyze the numerical results from the perspective of the dynamical group elements in Hamiltonians. Our findings highlight the importance of correlations in physical chaotic systems and provide insights into the deviations from RMT predictions. These understandings offer valuable directions for future research.