Constructible reality condition of pseudo entropy via pseudo-Hermiticity

We compute the pseudo entropy in two-dimensional holographic and free Dirac fermion CFTs for excited states under joining local quenches. Our analysis reveals two of its characteristic properties that are missing in the conventional entanglement entropy. One is that, under time evolution, the pseudo entropy exhibits a dip behavior as the excitations propagate from the joined point to the boundaries of the subsystem. The other is that the excess of pseudo entropy over entanglement entropy can be positive in holographic CFTs, whereas it is always non-positive in free Dirac fermion CFTs. We argue that the entropy excess can serve as a measure of multi-partite entanglement. Its positivity implies that the vacuum state in holographic CFTs possesses multi-partite entanglement, in contrast to free Dirac fermion CFTs.

Pseudo entropy under joining local quenches

Shinmyo,

Takayanagi,

Tasuki

2024

Entanglement phase transition in holographic pseudo entropy

Kanda,

Kawamoto,

Suzuki

et al. 2024

In this paper, we present holographic descriptions of entanglement phase transition using AdS/BCFT. First, we analytically calculate the holographic pseudo entropy in the AdS/BCFT model with a brane localized scalar field and show the entanglement phase transition behavior where the time evolution of entropy changes from the linear growth to the trivial one via a critical logarithmic evolution. In this model, the imaginary valued scalar field localized on the brane controls the phase transition, which is analogous to the amount of projections in the measurement induced phase transition. Next, we study the AdS/BCFT model with a brane localized gauge field, where the phase transition looks different in that there is no logarithmically evolving critical point. Finally, we discuss a bulk analog of the above model by considering a double Wick rotation of the Janus solution. We compute the holographic pseudo entropy in this model and show that the entropy grows logarithmically.

Pseudo entropy and pseudo-Hermiticity in quantum field theories

Guo,

Jiang

2024

In this paper, we explore the concept of pseudo Rényi entropy within the context of quantum field theories (QFTs). The transition matrix is constructed by applying operators situated in different regions to the vacuum state. Specifically, when the operators are positioned in the left and right Rindler wedges respectively, we discover that the logarithmic term of the pseudo Rényi entropy is necessarily real. In other cases, the result might be complex. We provide direct evaluations of specific examples within 2-dimensional conformal field theories (CFTs). Furthermore, we establish a connection between these findings and the pseudo-Hermitian condition. Our analysis reveals that the reality or complexity of the logarithmic term of pseudo Rényi entropy can be explained through this pseudo-Hermitian framework.Additionally, we investigate the divergent term of the pseudo Rényi entropy. Interestingly, we observe a universal divergent term in the second pseudo Rényi entropy within 2-dimensional CFTs. This universal term is solely dependent on the conformal dimension of the operator under consideration. For n-th pseudo Rényi entropy (n ≥ 3), the divergent term is intricately related to the specific details of the underlying theory.