BROTOCs and Quantum Information Scrambling at Finite Temperature

TL;DR

This paper introduces analytical and numerical studies of the bipartite regularized out-of-time-ordered correlator (BROTOC) at finite temperature, revealing its connections to quantum entanglement, purity, and dynamics in many-body systems.

Contribution

It provides the first analytical results for the bipartite regularized OTOC and explores its properties across different temperature regimes and its relation to quantum entanglement.

Findings

BROTOC quantifies the purity of the thermofield double state.

At infinite temperature, BROTOC relates to operator entanglement.

Numerical results distinguish between integrable and chaotic systems.

Abstract

Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature OTOC. We introduce analytical results for the bipartite regularized OTOC (BROTOC): the regularized OTOC averaged over random unitaries supported over a bipartition. We show that the BROTOC has several interesting properties, for example, it quantifies the purity of the associated thermofield double state and the operator purity of the analytically continued time-evolution operator. At infinite-temperature, it reduces to one minus the operator entanglement of the time-evolution operator. In the zero-temperature limit and for nondegenerate Hamiltonians, the BROTOC probes the groundstate entanglement. By computing long-time averages, we show that the equilibration value of the BROTOC is intimately related to eigenstate entanglement. Finally, we numerically study the equilibration value of the BROTOC for various physically relevant Hamiltonian models and comment on its ability to distinguish integrable and chaotic dynamics.