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arXiv:2006.04623 · Physical review. D/Physical review. D.

Bubble quenches in the AdS/BCFT model

Arthur G. Cavalcanti, Dmitry Melnikov

Published Feb 26, 2021• 0 citations
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Abstract

In this paper we construct time-dependent solutions of three-dimensional gravity in anti--de Sitter space dual to systems with boundaries (BCFTs), following the AdS/BCFT prescription. Such solutions can be discussed in the context of the dynamics of first-order phase transitions, or more generally, in the description of quantum quenches. As an example, we apply the holographic model to calculate the dynamics of the entanglement entropy of a local quench corresponding to a nucleation of a Euclidean bubble. As in the known $1+1$ conformal field theory examples of local cut and glue quenches, the holographic entanglement entropy grows logarithmically with time with the correct universal coefficient. However, in the bubble quench, the behavior is different at late times. The AdS/BCFT model exhibits the light-cone spreading of correlations and saturation at late times. We also find an analytical formula for the entropy at finite temperature. In the latter case, the initial logarithmic growth is followed by the linear law at intermediate times.

DOI
10.1103/physrevd.103.046022

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In this paper we construct time-dependent solutions of three-dimensional gravity in anti--de Sitter space dual to systems with boundaries (BCFTs), following the AdS/BCFT prescription. Such solutions can be discussed in the context of the dynamics of first-order phase transitions, or more generally, in the description of quantum quenches. As an example, we apply the holographic model to calculate the dynamics of the entanglement entropy of a local quench corresponding to a nucleation of a Euclidean bubble. As in the known 1+11+11+1 conformal field theory examples of local cut and glue quenches, the holographic entanglement entropy grows logarithmically with time with the correct universal coefficient. However, in the bubble quench, the behavior is different at late times. The AdS/BCFT model exhibits the light-cone spreading of correlations and saturation at late times. We also find an analytical formula for the entropy at finite temperature. In the latter case, the initial logarithmic growth is followed by the linear law at intermediate times.
In this paper we construct time-dependent solutions of three-dimensional gravity in AdS space dual to systems with boundaries (BCFTs), following the AdS/BCFT prescription. Such solutions can be discussed in the context of the dynamics of first order phase transitions, or more generally, in the description of quantum quenches. As an example, we apply the holographic model to calculate the dynamics of the entanglement entropy of a local quench corresponding to a nucleation of a Euclidean bubble. As in the known 1+1 CFT examples of local cut and glue quenches, the holographic entanglement entropy grows logarithmically with time with the correct universal coefficient. However, in the bubble quench, the behavior is different at late times. The AdS/BCFT model exhibits the light-cone spreading of correlations and saturation at late times. We also find an analytical formula for the entropy at finite temperature. In the latter case the initial logarithmic growth is followed by the linear law at intermediate times.
Abstract We study three different types of local quenches (local operator, splitting and joining) in both the free fermion and holographic CFTs in two dimensions. We show that the computation of a quantity called entanglement density, provides a systematic method to capture essential properties of local quenches. This allows us to clearly understand the differences between the free and holographic CFTs as well as the distinctions between three local quenches. We also analyze holographic geometries of splitting/joining local quenches using the AdS/BCFT prescription. We show that they are essentially described by time evolutions of boundary surfaces in the bulk AdS. We find that the logarithmic time evolution of entanglement entropy arises from the region behind the Poincaré horizon as well as the evolutions of boundary surfaces. In the CFT side, our analysis of entanglement density suggests such a logarithmic growth is due to initial non-local quantum entanglement just after the quench. Finally, by combining our results, we propose a new class of gravity duals, which are analogous to quantum circuits or tensor networks such as MERA, based on the AdS/BCFT construction.
A bstract 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.
Growth of entanglement entropy in time-dependent states formed due to a global quench in holographic conformal field theories which admit an Einstein-Gauss-Bonnet dual gravity description is studied. The global quench in the bulk is modelled by an AdS-Vaidya solution with an electric charge. It is observed that the Gauss-Bonnet correction parameter leads to faster thermalization, and lower saturation entropy. The rate of growth also depends crucially on the correction, and may exceed 1 in general spacetime dimensions. Nevertheless, the growth still follows the universal pattern expected for relativistic CFTs. Additionally, a time-dependent analogue of relative entropy introduced in [1] is generalized to include correction from the Gauss-Bonnet parameter. We demonstrate our findings through concrete examples, including instantaneous, linear, and periodically driven quenches. We also briefly mention the evolution of mutual information.
Based on the studies of pseudoentropy in de Sitter, there have been recent proposals for a timelike entanglement in AdS/CFT. In this work, we explore this proposal in the context of a holographic CFT undergoing a global quench. We study various cases in which the timelike intervals are anchored at various boundary times, sometimes straddling the infalling shell. The early and late time behaviors reproduce the known results coming from the pure AdS and the black hole geometry dual to the thermal CFT state respectively. However when the infalling shock straddles the timelike interval, the dynamics drastically differs from how the entanglement entropy evolves.
Abstract We study the entanglement entropy for time-like subsystem in two-dimensional boundary conformal field theory (BCFT) both from the field theory and holographic point of view. In field theory, we compute the time-like entanglement entropy of a pure time-like interval at zero and finite temperature using the replica technique and analytical continuation. We find that, similar to the ordinary space-like entanglement entropy in BCFT, the time-like entropy also has a bulk phase and a boundary phase which corresponds respectively to the dominance of the identity block in the bulk and boundary OPE channels. However, we find that in Lorentzian BCFT, the time-like entanglement entropy posses a third Regge phase which arises in the Regge limit of the interval, when one endpoint of the time interval approaches the light cone of the mirror image of the other endpoint. We determine the phase diagram for the time-like entanglement entropy. We find that while the time-like entropy is complex in the bulk phase and has a boundary term in the boundary phase, there is no boundary entropy in the Regge phase. Moreover, it can be real or complex depending on which side the Regge limit is approached from. On the gravity side, we obtain the holographic time-like entanglement entropy from the corresponding bulk dual geometries and find exact agreement with the field theory results. The time-like entanglement entropy may be useful to describe the entanglement of a quantum dot on a half line.