Pseudo Entropy in Free Quantum Field Theories
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 and dynamical exponent . 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.
Cite
@article{arxiv.2011.09648,
title = {Pseudo Entropy in Free Quantum Field Theories},
author = {Ali Mollabashi and Noburo Shiba and Tadashi Takayanagi and Kotaro Tamaoka and Zixia Wei},
journal= {arXiv preprint arXiv:2011.09648},
year = {2021}
}
Comments
7 pages, revtex, 5 figures + 22 pages supplementary material. v2: minor improvements, matches PRL version