Aspects of pseudoentropy in field theories

Abstract

In this paper, we explore properties of pseudoentropy in quantum field theories and spin systems from several approaches. pseudoentropy is a generalization of entanglement entropy such that it depends on both an initial and final state and has a clear gravity dual via the AdS/CFT. We numerically analyze a class of free scalar field theories and the XY spin model. This reveals basic properties of pseudoentropy in quantum many-body systems, namely, the area-law behavior, the saturation behavior, and the nonpositivity of difference between the pseudoentropy and averaged entanglement entropy in the same quantum phase. In addition, our numerical analysis finds an example where the strong subadditivity of pseudoentropy gets violated. Interestingly, we find that the nonpositivity of the difference can be violated only if the initial and final state belong to different quantum phases. We also present analytical arguments, which support these properties by both conformal field theoretic and holographic calculations. When the initial and final state belong to different topological phases, we expect a gapless mode localized along an interface, which enhances the pseudoentropy, leading to the violation of the nonpositivity of the difference. Moreover, we also compute the time evolution of pseudoentropy after a global quantum quench, where we observe that the imaginary part of pseudoentropy shows an interesting characteristic behavior.