Abstract
In this article, we explore properties of pseudo entropy [1] in quantum field theories and spin systems from several approaches. Pseudo entropy 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 the basic properties of pseudo entropy in many-body systems, namely, the area law behavior, the saturation behavior, and the non-positivity of difference between the pseudo entropy and averaged entanglement entropy in the same quantum phase. In addition, our numerical analysis finds an example where the strong subadditivity of pseudo entropy gets violated. Interestingly we find that the non-positivity of the difference can be violated only if the initial and final states 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 states belong to different topological phases, we expect a gapless mode localized along an interface, which enhances the pseudo entropy leading to the violation of the non-positivity of the difference. Moreover, we also compute the time evolution of pseudo entropy after a global quench, were we observe that the imaginary part of pseudo entropy shows interesting characteristc behavior.
Highlights
As one of the most fundamental quantum resources, entanglement plays key roles in almost all areas of quantum physics, practically and theoretically
S12 is always nonpositive when |ψ1 and |ψ2 are in the same quantum phase, while it tends to be positive when |ψ1 and |ψ2 are in different quantum phases
We will see in the following numerical results that S12 0 if |ψ1 and |ψ2 are in the same quantum phase
Summary
As one of the most fundamental quantum resources, entanglement plays key roles in almost all areas of quantum physics, practically and theoretically. Pseudoentropy is clearly an important fundamental quantity in general quantum systems. It is shown in [12] that pseudoentropy can be regarded as the number of Bell pairs that one can distill from a post-selection process for a specific class of transition matrices. This paper is an extended version of [15] with all the technical details presented It includes many new results on different types of factorization, fermionic systems, quantum phase transitions, dynamical setups, and holographic setups. For states near the ground state of QFT and for holographic states, S(τA1|2) satisfies an area law These properties will be verified for multiple times in different systems in this paper. We will summarize the main results contained in this paper and show a road map, which is useful to read this paper
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