Aspects of Pseudo Entropy in Field Theories

TL;DR

This paper investigates pseudo entropy in quantum field theories and spin systems, revealing its properties, violations of inequalities, and behavior under various conditions, supported by numerical and analytical methods including holography.

Contribution

It provides the first comprehensive analysis of pseudo entropy in many-body systems, including numerical, analytical, and holographic insights into its properties and violations.

Findings

Pseudo entropy follows an area law in many-body systems.

Violations of strong subadditivity of pseudo entropy are observed.

Differences in pseudo entropy can violate non-positivity when states are in different phases.

Abstract

In this article, we explore properties of pseudo entropy [1] in quantum field theories and spin systems from several approaches. Pseudo entropy is a generalization of entanglement entropy such that it depends on both an initial and final state and has a clear gravity dual via the AdS/CFT. We numerically analyze a class of free scalar field theories and the XY spin model. This reveals the basic properties of pseudo entropy in many-body systems, namely, the area law behavior, the saturation behavior, and the non-positivity of difference between the pseudo entropy and averaged entanglement entropy in the same quantum phase. In addition, our numerical analysis finds an example where the strong subadditivity of pseudo entropy gets violated. Interestingly we find that the non-positivity of the difference can be violated only if the initial and final states belong to different quantum phases. We also present analytical arguments which support these properties by both conformal field theoretic and holographic calculations. When the initial and final states belong to different topological phases, we expect a gapless mode localized along an interface, which enhances the pseudo entropy leading to the violation of the non-positivity of the difference. Moreover, we also compute the time evolution of pseudo entropy after a global quench, were we observe that the imaginary part of pseudo entropy shows interesting characteristc behavior.