Entanglement Phase Transition in Holographic Pseudo Entropy

TL;DR

This work advances the holographic understanding of entanglement phase transitions by studying pseudo entropy in AdS/BCFT with brane-localized scalar fields and gauge fields, and by introducing a bulk Janus construction as a dissipative, transition-matrix analog in holography.The authors demonstrate a three-regime dynamical structure: linear growth in the BTZ phase, a critical logarithmic growth at Δφ = Δφ_*, and a finite saturation beyond the critical point, with precise coefficients tied to the BCFT central charge and brane data.Higher-dimensional extensions remove the intermediate logarithmic regime, while null-energy considerations reveal NEC violation in the dissipative brane setups, linking gravitational backreaction to non-unitary boundary dynamics.Complementary CFT analyses of pseudo Rényi entropy and a gauge-field brane setup enrich the correspondence, and a bulk soft-wall/Janus model extends the framework beyond end-of-the-world branes, illustrating defect-driven modulation of entanglement in both Euclidean and Lorentzian settings.

Abstract

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.

Figures (36)

• Figure 2.1.1: A sketch of the AdS/BCFT model. The left figure shows a BCFT defined on a strip (light grey region) with the width $\frac{\beta}{2}$. The right figure shows the dual gravity setup which is given by the AdS$_3$ region surrounded by the strip and the EOW brane (blue surface). The red curve $\Gamma_A$ is the geodesic whose length calculates the holographic pseudo entanglement entropy for the subregion $A$ shaded in green.
• Figure 2.1.2: A sketch of gravity duals in our AdS/BCFT model with a brane localized scalar. Depending on the value of the shift of scalar field $\Delta \phi$, there are three phases (a) BTZ phase, (b) Poincaré phase and (c) TAdS phase. The upper three pictures describe the Euclidean geometries, while the lower three are the corresponding Lorentzian time evolution obtained from analytic continuation.
• Figure 2.2.1: The EOW branes in the $\Delta \phi$ phase. It is conformally compactified using arctan. The lower square corresponds to the original BTZ black hole, while the upper one corresponds to the extended region. In this picture, the dual BCFT lives in the left asymptotic boundary of the lower BTZ. The EOW brane with $z_0/a= 1$, corresponding to $\Delta \phi=0$, forms a vertical line, which is consistent with the configuration described in Hartman:2013qma.
• Figure 2.2.2: Graphs of entropy behavior. Left: $t$-dependency, i.e., we fix $a=1$ and $z_0=0.5.$ Middle: $z_0$-dependency, i.e., fix $a=1$ and $t=10.$ Right: $\Delta\phi$-dependency, i.e., fix $\beta=1$ and $t=10.$ For all graphs, we set $\epsilon=10^{-5}.$
• Figure 2.3.1: Brane configurations with $\phi^\prime=0.$ These correspond to constant tension branes without the brane scalar.