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arXiv:2403.12086

Surface growth approach for bulk reconstruction in AdS/BCFT correspondence

Fang, Xihao, Chen, Fangzhong, J. R. Sun

Published Mar 10, 2024• 0 citations
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Abstract

In this paper, we extend the surface growth scheme in AdS spacetime with a boundary in the AdS/BCFT correspondence. We show that the entanglement wedge with a boundary can be constructed from the direct growth of bulk extremal surfaces layer by layer. In addition, we find that the surface growth configuration in BCFT can be connected with the defect multi scale entanglement renormalization ansatz (MERA) tensor network. Furthermore, we also investigate the entanglement of purification within the surface growth process, which reveals more refined structure of entanglement entropy and indicates a selection rule for surface growth in the bulk reconstruction.

DOI
10.48550/arxiv.2403.12086

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In this paper, we extend the surface growth scheme in AdS spacetime with a boundary in the AdS/BCFT correspondence. We show that the entanglement wedge with a boundary can be constructed from the direct growth of bulk extremal surfaces layer by layer. In addition, we find that the surface growth configuration in BCFT can be connected with the defect multi scale entanglement renormalization ansatz (MERA) tensor network. Furthermore, we also investigate the entanglement of purification within the surface growth process, which reveals more refined structure of entanglement entropy and indicates a selection rule for surface growth in the bulk reconstruction.
Abstract In this study, we extend the surface growth approach for bulk reconstruction into the AdS spacetime with a boundary in the AdS/BCFT correspondence. We show that the geometry in the entanglement wedge with a boundary can be constructed from the direct growth of bulk extremal surfaces layer by layer. Furthermore, we observe that the surface growth configuration in BCFT can be connected with the defect multi scale entanglement renormalization ansatz (MERA) tensor network. Additionally, we investigate the entanglement of purification within the surface growth process, which not only reveals more refined structure of entanglement entropy in the entanglement wedge but also suggests a selection rule for surface growth in the bulk reconstruction.
Abstract We propose a surface growth approach to reconstruct the bulk spacetime geometry, motivated by Huygens’ principle of wave propagation. We show that our formalism can be explicitly realized with the help of the surface/state correspondence and the one-shot entanglement distillation (OSED) method. We first construct a tensor network corresponding to a special surface growth picture with spherical symmetry and fractal feature using the OSED method and show that the resulting tensor network can be identified with the MERA-like tensor network, which gives a proof that the MERA-like tensor network is indeed a discretized version of the time slice of AdS spacetime, rather than just an analogy. Furthermore, we generalize the original OSED method to describe more general surface growth picture by using of the surface/state correspondence and the generalized RT formula, which leads to a more profound interpretation for the surface growth process and provides a concrete and intuitive way for the idea of entanglement wedge reconstruction.
Abstract In this paper, we show using several examples that the bulk geometry of asymptotically AdS spacetimes can be effectively reconstructed using an intuitive and visual method called the surface growth scheme. This new approach for bulk reconstruction was originally proposed in a recent paper, along with its explicit realization using the one-shot entanglement distillation tensor network and the surface/state correspondence. In this paper, we directly analyze the growth of the bulk minimal surfaces to implement this scheme. Our study provides further support for the surface growth approach in entanglement wedge reconstruction.
The multiscale entanglement renormalization ansatz (MERA) is a tensor network that provides an efficient way of variationally estimating the ground state of a critical quantum system. The network geometry resembles a discretization of spatial slices of an anti--de Sitter (AdS) spacetime and ``geodesics'' in the MERA reproduce the Ryu-Takayanagi formula for the entanglement entropy of a boundary region in terms of bulk properties. It has therefore been suggested that there could be an AdS/MERA correspondence, relating states in the Hilbert space of the boundary quantum system to ones defined on the bulk lattice. Here we investigate this proposal and derive necessary conditions for it to apply, using geometric features and entropy inequalities that we expect to hold in the bulk. We show that, perhaps unsurprisingly, the MERA lattice can only describe physics on length scales larger than the AdS radius. Further, using the covariant entropy bound in the bulk, we show that there are no conventional MERA parameters that completely reproduce bulk physics even on super-AdS scales. We suggest modifications or generalizations of this kind of tensor network that may be able to provide a more robust correspondence.
A bstract In the AdS/CFT correspondence, the causal structure of the bulk AdS spacetime is tied to entanglement in the dual CFT. This relationship is captured by the connected wedge theorem [1], which states that a bulk scattering process implies the existence of O (1/ G N ) entanglement between associated boundary subregions. In this paper, we study the connected wedge theorem in two asymptotically AdS 2+1 spacetimes: the conical defect and BTZ black hole geometries. In these settings, we find that bulk scattering processes require not just large entanglement, but also additional restrictions related to candidate RT surfaces which are non-minimal. We argue these extra relationships imply a certain CFT entanglement structure involving internal degrees of freedom. Because bulk scattering relies on sub-AdS scale physics, this supports the idea that sub-AdS scale locality emerges from internal degrees of freedom. While the new restriction that we identify on non-minimal surfaces is stronger than the initial statement of the connected wedge theorem, we find that it is necessary but still not sufficient to imply bulk scattering in mixed states.
We consider a composite system where AdS3_33​ gravity is coupled to a flat heat bath and investigate the mutual information between two subregions on the intersection of the AdS3_33​ and bath, referred to as the boundary mutual information (BMI). The corresponding entanglement entropy is captured via quantum extremal surfaces (QES), which holographically be computed by a surface optimization algorithm based on ``Surface Evolver''. We focus on both connected and disconnected configurations of the quantum entanglement wedge (Q-EW) in the AdS3_33​ bulk and analyze the finite corrections to the BMI. Our numerical results reveal a phase transition of the BMI as the separation between two subregions increases. Furthermore, we find that the BMI can naturally be decomposed into two distinct components: a geometric term arising from the areas of the quantum extremal surfaces, and a correction term resulting from bulk quantum fields within the Q-EW. Interestingly, the geometric contribution always exceeds the total BMI, indicating a negative correction from the bulk matter fields. This negativity can be understood as the result of subtracting a greater contribution from quantum fields in the connected Q-EW than in the disconnected one. We also reproduce the negative contribution of bulk quantum fields to BMI within a random tensor network (RTN) toy model of double holography. Modeling the bulk as a highly mixed state entangled with a large bath leads to a volume-law bulk entropy. In the large bond-dimension limit, the geometric part of the BMI remains non-negative, while the bulk entropy contribution becomes non-positive when the Q-EWs merge.