Pseudo Entropy in Free Quantum Field Theories

• URL: http://arxiv.org/abs/2011.09648v2
• Date: Wed, 13 Jan 2021 02:59:45 GMT
• Title: Pseudo Entropy in Free Quantum Field Theories
• Authors: Ali Mollabashi, Noburo Shiba, Tadashi Takayanagi, Kotaro Tamaoka, and Zixia Wei
• Abstract summary: We conjecture two novel properties of Pseudo entropy which we conjecture to be universal in field theories. Our numerical results imply that pseudo entropy can play a role as a new quantum order parameter.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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