Constructible reality condition of pseudo entropy via pseudo-Hermiticity

Guo, Wu-zhong; He, Song; Zhang, Yu-Xuan

doi:10.1007/JHEP05(2023)021

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Constructible reality condition of pseudo entropy via pseudo-Hermiticity

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He, Song
Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Guo, W.-z., He, S., & Zhang, Y.-X. (2023). Constructible reality condition of pseudo entropy via pseudo-Hermiticity. Journal of High Energy Physics, 2023(05): 021. doi:10.1007/JHEP05(2023)021.

Cite as: https://hdl.handle.net/21.11116/0000-000B-231A-1

Abstract

As a generalization of entanglement entropy, pseudo entropy is not always
real. The real-valued pseudo entropy has promising applications in holography
and quantum phase transition. We apply the notion of pseudo-Hermticity to
formulate the reality condition of pseudo entropy. We find the general form of
the transition matrix for which the eigenvalues of the reduced transition
matrix possess real or complex pairs of eigenvalues. Further, we construct a
class of transition matrices for which the pseudo (R\'enyi) entropies are
positive. Some known examples which give real pseudo entropy in quantum field
theories can be explained in our framework. Our results offer a novel method to
generate the transition matrix with real pseudo entropy. Finally, we show the
reality condition for pseudo entropy is related to the Tomita-Takesaki modular
theory for quantum field theory.