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On Holographic Time-Like Entanglement Entropy

M. M. Daryaei Goki, M. Ali-Akbari

TL;DR

The paper investigates holographic time-like entanglement entropy (HTEE) and quantum pseudo-entropy under thermal-to-anisotropic transitions. It combines a quantum-mechanical two-qubit toy model for pseudo-entropy with holographic calculations in an anisotropic AdS$_5$ background to compare their responses to spatial-temporal anisotropy. Key findings include that the imaginary part of pseudo-entropy vanishes in isotropic or high-temperature limits unless complex anisotropy is introduced, and that HTEE's imaginary part exhibits similar sensitivity but depends on how anisotropy is implemented in the bulk. Both quantities tend to decrease with modest anisotropy at fixed temperature, but at larger anisotropy they can reorganize, including sign changes and cancellations, highlighting nuanced differences between pseudo-entropy and HTEE as diagnostics of strongly coupled dynamics.

Abstract

In this paper, we compare and analyze holographic timelike entanglement entropy with pseudo-entropy in quantum mechanics for a two-qubit system, considering transitions from a thermal state to an anisotropic thermal state at fixed temperature. We identify several common properties but also report important differences between these quantities.

On Holographic Time-Like Entanglement Entropy

TL;DR

The paper investigates holographic time-like entanglement entropy (HTEE) and quantum pseudo-entropy under thermal-to-anisotropic transitions. It combines a quantum-mechanical two-qubit toy model for pseudo-entropy with holographic calculations in an anisotropic AdS background to compare their responses to spatial-temporal anisotropy. Key findings include that the imaginary part of pseudo-entropy vanishes in isotropic or high-temperature limits unless complex anisotropy is introduced, and that HTEE's imaginary part exhibits similar sensitivity but depends on how anisotropy is implemented in the bulk. Both quantities tend to decrease with modest anisotropy at fixed temperature, but at larger anisotropy they can reorganize, including sign changes and cancellations, highlighting nuanced differences between pseudo-entropy and HTEE as diagnostics of strongly coupled dynamics.

Abstract

In this paper, we compare and analyze holographic timelike entanglement entropy with pseudo-entropy in quantum mechanics for a two-qubit system, considering transitions from a thermal state to an anisotropic thermal state at fixed temperature. We identify several common properties but also report important differences between these quantities.
Paper Structure (5 sections, 32 equations, 3 figures)

This paper contains 5 sections, 32 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Pseudo-entropy in quantum mechanics: A toy model
  3. Review on the background
  4. Holographic timeLike entanglement entropy
  5. Numerical results

Figures (3)

  • Figure 1: The imaginary part of the pseudo-entropy $S_{pA}^I$ is plotted as a function of $\beta\vert\Delta\vert$ for $\beta=10$ and $0\le\Delta_x\le 2$, left panel: $\ \delta_x=1,\ \delta_y=0$ and $\Delta_y=1$ (red) or $\Delta_y=-1$ (blue, dashed) and right panel: $\ \delta_x=-1,\ \delta_y=1.1$ and $\Delta_y=1$ (red) or $\Delta_y=-1$ (blue, dashed). Two opposite behaviors arise depending on the sign of the anisotropy parameter $\Delta_y$.
  • Figure 2: The real and imaginary parts of the HTEE are shown for $T_0=0.16$, $T=2.30$, $a=7.674$ and $c=10^6$.
  • Figure 3: The real and imaginary parts of the HTEE are shown for $T_0 = 0.08$ and $c=10^7$, Left: $T = 10$ and Right: $T=2.3$. In the left panel, $aT^{-1} \ll 1$, while in the right panel, $a$ is arbitrary. The continuous curves correspond to the fitted functions $\widehat{S}_{tR} \propto a^2$ and $\widehat{S}_{tI} \propto a^2$.