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CFT derivation of entanglement phase transition in pseudo entropy

Hiroki Kanda, Tadashi Takayanagi, Zixia Wei

Abstract

In this paper, we discuss the entanglement phase transition of pseudo entropy in CFTs. We focus on the case where the in-state and the out-state are different boundary states related by boundary condition changing operators. We compute the pseudo entropy with BCFT methods and find a phase transition with respect to the conformal weight of the boundary condition changing operators. For holographic CFTs, we confirm that the CFT results match that evaluated in AdS.

CFT derivation of entanglement phase transition in pseudo entropy

Abstract

In this paper, we discuss the entanglement phase transition of pseudo entropy in CFTs. We focus on the case where the in-state and the out-state are different boundary states related by boundary condition changing operators. We compute the pseudo entropy with BCFT methods and find a phase transition with respect to the conformal weight of the boundary condition changing operators. For holographic CFTs, we confirm that the CFT results match that evaluated in AdS.
Paper Structure (13 sections, 80 equations, 5 figures)

This paper contains 13 sections, 80 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Entanglement Pseudo Transition in Holographic CFTs
  3. Analysis in Euclidean Setup
  4. Lorentzian evolution in Holographic CFT
  5. Small deformation phase $0<h_{\Psi}<\frac{c}{24}$
  6. Critical phase $h_{\Psi}=\frac{c}{24}$
  7. Large deformation phase $h_{\Psi}>\frac{c}{24}$
  8. Pseudo entropy in Dirac fermions CFT
  9. Conclusions and Discussions
  10. Computations in Dirac Fermion CFT
  11. Replica method and bosonization
  12. Scalar field description
  13. Computing pseudo entropy

Figures (5)

  • Figure 2.0.1:
  • Figure 2.0.2:
  • Figure 2.2.1: The Euclidean BTZ geometry. This has a conical singularity with $\tau$-direction
  • Figure 2.2.2: There are two candidates of geodesics, which are complex conjugate to each other in the Lorentzian space
  • Figure 2.2.3: A sketch of gravity dual of the large deformation phase (left) and the profile of geodesic (right). This dual geometry is an universal covering of usual thermal AdS.