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arXiv:1905.06808 · Physics Letters B

The effect of anisotropy on holographic entanglement entropy and mutual information

Peng Liu, Chao Niu, Jian-Pin Wu

Published Jul 17, 2019• 17 citations
arXivHTMLPDF

Abstract

We study the effect of anisotropy on holographic entanglement entropy (HEE) and holographic mutual information (MI) in the Q-lattice model, by exploring the HEE and MI for infinite strips along arbitrary directions. We find that the lattice always enhances the HEE. The MI, however, is enhanced by lattice for large sub-regions; while for small sub-regions, the MI is suppressed by the lattice. We also discuss how these phenomena result from the deformation of geometry caused by Q-lattices.

DOI
10.1016/j.physletb.2019.07.035

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We study the effect of anisotropy on holographic entanglement entropy (HEE) and holographic mutual information (MI) in the Q-lattice model, by exploring the HEE and MI for infinite strips along arbitrary directions. We find that the lattice always enhances the HEE. The MI, however, is enhanced by lattice for large sub-regions; while for small sub-regions, the MI is suppressed by the lattice. We also discuss how these phenomena result from the deformation of geometry caused by Q-lattices.
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Abstract We study the mixed state entanglement in a holographic axion model. We find that the holographic entanglement entropy (HEE), mutual information (MI) and entanglement of purification (EoP) exhibit very distinct behaviors with system parameters. The HEE exhibits universal monotonic behavior with system parameters, while the behaviors of MI and EoP relate to the specific system parameters and configurations. We find that MI and EoP can characterize mixed state entanglement better than HEE since they are less affected by thermal effects. Specifically, the MI partly cancels out the thermal entropy contribution, while the holographic EoP is not dictated by the thermal entropy in any situation. Moreover, we argue that EoP is more suitable for describing mixed state entanglement than MI. Because the MI of large configurations are still dictated by the thermal entropy, while the EoP will never be controlled only by the thermal effects.
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The entanglement exhibits extremal or singular behavior near quantum critical points (QCPs) in many condensed matter models. These intriguing phenomena, however, still call for a widely accepted understanding. In this paper we study this issue in holographic framework. We investigate the connection between the holographic entanglement entropy (HEE) and the quantum phase transition (QPT) in a lattice-deformed Einstein-Maxwell-Dilaton theory. Novel backgrounds exhibiting metal-insulator transitions (MIT) have been constructed in which both metallic phase and insulating phase have vanishing entropy density in zero temperature limit. We find that the first order derivative of HEE with respect to lattice parameters exhibits extremal behavior near QCPs. We propose that it would be a universal feature that HEE or its derivatives with respect to system parameters can characterize QPT in a generic holographic system. Our work opens a window for understanding the relation between entanglement and the QPT from a holographic perspective.
Nonlocal interactions are known to generate volume-law entanglement entropy. However, their deeper impact on the fine structure of quantum correlations remains a key open question. In this work, we explore a bosonic nonlocal field theory, examining correlation measures beyond entanglement entropy, namely, mutual information and tripartite information. Using numerical lattice simulations, we show that the nonlocality scale, AAA, not only determines the onset of volume-law behavior but also leads to striking features: notably, extremely long-range mutual information and an unusual monogamy structure. In this regime, increasing the separation between large regions can paradoxically enhance their multipartite entanglement. Through holographic duality, we verify that the Ryu-Takayanagi formula correctly captures the volume-law scaling of entropy. Yet, a significant tension emerges: while the field theory reveals rich spatial correlations, the holographic model predicts a complete suppression of both mutual and tripartite information in the volume-law phase. This non-monogamous behavior in the holographic description stands in sharp contrast to the monogamous and highly structured entanglement observed in the field theory. Our results demonstrate that nonlocality gives rise to quantum states of such complexity that conventional geometric models of spacetime fall short. This points to the need for a new framework that goes beyond geometry to fully capture the nature of these correlations.