Subregion Spectrum Form Factor via Pseudo Entropy

TL;DR

This paper introduces a subsystem generalization of the spectral form factor using pseudo entropy in 2D conformal field theories, revealing its time evolution and theory dependence.

Contribution

It presents a novel approach to analyze spectral form factors via pseudo entropy, extending the concept to subsystems in conformal field theories.

Findings

Pseudo entropy's real part mimics spectral form factor behavior.

Pseudo entropy starts at thermal entropy, dips, then recovers.

Behavior varies with different theories on compact spaces.

Abstract

We introduce a subsystem generalization of the spectral form factor via pseudo entropy, the von-Neumann entropy for the reduced transition matrix. We consider a transition matrix between the thermofield double state and its time-evolved state in two-dimensional conformal field theories, and study the time-dependence of the pseudo entropy for a single interval. We show that the real part of the pseudo entropy behaves similarly to the spectral form factor; it starts from the thermal entropy, initially drops to the minimum, then it starts increasing, and finally approaches the vacuum entanglement entropy. We also study the theory-dependence of its behavior by considering theories on a compact space.