On the real-time evolution of pseudo-entropy in 2d CFTs

Abstract

In this work, we study the real-time evolution of pseudo-(Rényi) entropy, a generalization of entanglement entropy, in two-dimensional conformal field theories (CFTs). We focus on states obtained by acting primary operators located at different space points or their linear combinations on the vacuum. We show the similarities and differences between the pseudo-(Rényi) entropy and entanglement entropy. For excitation by a single primary operator, we analyze the behaviors of the 2nd pseudo-Rényi entropy in various limits and find some symmetries associated with the subsystem and the positions of the insertion operators. For excitation by linear combinations, the late time limit of the $n$th pseudo-Rényi entropy shows a simple form related to the coefficients of the combinations and Rényi entropy of the operators, which can be derived by using the Schmidt decomposition. Further, we find two kinds of particular spatial configurations of insertion operators in one of which the pseudo-(Rényi) entropy remains real throughout the time evolution.

arXiv comment34 pages, 7 figures, 1 table v2: typos corrected, references added

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Cited by in corpus (12)

• Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy
• Timelike entanglement entropy
• Constructible reality condition of pseudo entropy via pseudo-Hermiticity
• SVD Entanglement Entropy
• Entanglement Phase Transition in Holographic Pseudo Entropy
• Pseudo entropy under joining local quenches
• Holographic Timelike Entanglement Entropy from Rindler Method
• Relation between time- and spacelike entanglement entropy
• Sum rule for the pseudo-Rényi entropy
• Pseudo entropy and pseudo-Hermiticity in quantum field theories
• Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point
• Detecting quantum chaos via pseudo-entropy