Entanglement patterns of quantum chaotic Hamiltonians with a scalar U(1) charge

TL;DR

This paper develops a new approach to describe the detailed entanglement patterns of eigenstates in quantum chaotic many-body systems with local interactions and conserved charges, emphasizing the role of spatial locality.

Contribution

It introduces constrained random state ensembles incorporating locality and symmetries to analytically and numerically capture entanglement fluctuations in quantum chaotic Hamiltonians.

Findings

Accurately describes entanglement patterns beyond volume-law using constrained random states.

Highlights the importance of spatial locality in universal eigenstate features.

Provides analytical and numerical evidence for entanglement fluctuations.

Abstract

Our current understanding of quantum chaos in many-body quantum systems hinges on the random matrix theory(RMT) behavior of eigenstates and their energy level statistics. Although RMT has been remarkably successful in describing `coarse' features of many-body quantum Hamiltonians in chaotic regimes, such as the Wigner-Dyson level spacing statistics or the volume-law behavior of eigenstate entanglement entropy, it remains a challenge to describe their `finer' features, particularly those arising from spatial locality. Here, we show that we can accurately describe the statistical behavior of eigenstate ensembles in many-body Hamiltonians by using pure random states with physical constraints that capture the essential features of the Hamiltonian, specifically spatial locality and symmetries. We demonstrate our approach on local spin Hamiltonians with a scalar U(1) charge. By constructing ensembles of constrained random states that account for two commuting scalar charges playing the role of energy and magnetization, we describe the patterns of entanglement of mid-spectrum eigenstates beyond their average volume-law behavior, including $O(1)$ corrections and fluctuations, analytically and numerically. When defining the correspondence between quantum chaotic eigenstates in many-body Hamiltonians and RMT ensembles, our work highlights the important role played by spatial locality in describing universal features beyond the volume-law behavior.