Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models

TL;DR

This paper explores how disorder affects quantum chaos, delocalization, and entanglement in Heisenberg spin models, revealing correlations that could serve as new diagnostics for quantum chaos.

Contribution

It introduces a measure of relative delocalization and investigates the interplay between entanglement, delocalization, and chaos in disordered Heisenberg models, highlighting basis dependence and new diagnostic tools.

Findings

Correlation between entanglement, delocalization, and integrability identified

Proposed a basis-independent measure of relative delocalization

Analytical estimates align with random matrix theory predictions

Abstract

We investigate disordered one- and two-dimensional Heisenberg spin lattices across a transition from integrability to quantum chaos from both a statistical many-body and a quantum-information perspective. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implications of basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of {\em relative delocalization} is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and {\em generalized entanglement} are investigated in a wide parameter regime by using a family of spin- and fermion- purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive {\em correlation between entanglement, delocalization, and integrability} is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.