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 $m$ 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.

7 pages, revtex, 5 figures + 22 pages supplementary material. v2: minor improvements, matches PRL version

References in corpus (5)

• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Thermodynamical Property of Entanglement Entropy for Excited States
• Spatial structures and localization of vacuum entanglement in the linear harmonic chain
• Ten-dimensional supersymmetric Janus solutions
• Entanglement Entropy of Disjoint Regions in Excited States : An Operator Method

Cited by in corpus (4)

• Aspects of Pseudo Entropy in Field Theories
• Topological pseudo entropy
• On the real-time evolution of pseudo-entropy in 2d CFTs
• Pseudo complexity of purification for free scalar field theories