Pseudo Entropy in Free Quantum Field Theories

TL;DR

This paper investigates pseudo entropy in free quantum field theories and spin chains, revealing universal properties like saturation and non-positivity, and proposing its use as a quantum phase transition indicator.

Contribution

It extends the Gaussian method for pseudo entropy in free scalar theories and uncovers two universal properties, enhancing understanding of pseudo entropy in quantum field theories.

Findings

Pseudo entropy exhibits saturation behavior.

Difference between pseudo entropy and averaged entanglement entropy is non-positive.

Pseudo entropy can serve as a quantum order parameter.

Abstract

Pseudo entropy is an interesting quantity with a simple gravity dual, which generalizes entanglement entropy such that it depends on both an initial and a final state. Here we reveal the basic properties of pseudo entropy in quantum field theories by numerically calculating this quantity for a set of two-dimensional free scalar field theories and the Ising spin chain. We extend the Gaussian method for pseudo entropy in free scalar theories with two parameters: mass $m$ and dynamical exponent $z$. This computation finds two novel properties of Pseudo entropy which we conjecture to be universal in field theories, in addition to an area law behavior. One is a saturation behavior and the other one is non-positivity of the difference between pseudo entropy and averaged entanglement entropy. Moreover, our numerical results for the Ising chain imply that pseudo entropy can play a role as a new quantum order parameter which detects whether two states are in the same quantum phase or not.