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arXiv:1502.03661 · Journal of High Energy Physics

Holographic entanglement entropy close to quantum phase transitions

Yi Ling, Peng Liu, Chao Niu, Jian-Pin Wu, Zhuo-Yu Xian

Published Apr 1, 2016• 54 citations
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Abstract

We investigate the holographic entanglement entropy (HEE) of a strip geometry in four dimensional Q-lattice backgrounds, which exhibit metal-insulator transitions in the dual field theory. Remarkably, we find that the HEE always displays a peak in the vicinity of the quantum critical points. Our model provides the first direct evidence that the HEE can be used to characterize the quantum phase transition (QPT). We also conjecture that the maximization behavior of HEE at quantum critical points would be universal in general holographic models.

DOI
10.1007/jhep04(2016)114

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We investigate the holographic entanglement entropy (HEE) of a strip geometry in four dimensional Q-lattice backgrounds, which exhibit metal-insulator transitions in the dual field theory. Remarkably, we find that the HEE always displays a peak in the vicinity of the quantum critical points. Our model provides the first direct evidence that the HEE can be used to characterize the quantum phase transition (QPT). We also conjecture that the maximization behavior of HEE at quantum critical points would be universal in general holographic models.
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.
Abstract We investigate the behavior of the holographic entanglement entropy (HEE) in proximity to the quantum critical points (QCPs) of the metal-insulator transition (MIT) in the Einstein–Maxwell-dilaton-axions (EMDA) model. Since both the metallic phase and the insulating phase are characterized by distinct IR geometries, we used to expect that the HEE itself characterizes the QCPs. This expectation is validated for certain cases, however, we make a noteworthy observation: for a specific scenario where −1<γ≤−1/3-1<\gamma \le -1/3−1<γ≤−1/3 - 1 < γ ≤ - 1 / 3 , with γ\gamma γ γ as a coupling parameter, it is not the HEE itself but rather the second-order derivative of HEE with respect to the lattice wave number that effectively characterizes quantum phase transitions (QPTs). This distinction arises due to the influence of thermal effects. These findings present novel insights into the interplay between HEE and QPTs in the context of the MIT, and have significant implications for studying QPTs at finite temperatures.
Abstract We study quantum criticality in a holographic Einstein–Maxwell–Dilaton–Axion (EMDA) p-wave superconductor exhibiting a superconductor–insulator transition (SIT). By tracking the superconducting energy gap, we show that approaching the quantum critical point (QCP) closes the gap and induces incipient insulating features, indicating that enhanced quantum fluctuations suppress superconducting order and trigger the SIT. We suggest that this behavior occurs only when the condensate orientation is aligned with the direction of translational symmetry breaking. To probe the transition, we employ two holographic indicators: holographic entanglement entropy (HEE) and the entanglement wedge cross-section (EWCS), the latter being a mixed-state entanglement measure. In contrast to HEE, which for sufficiently large configuration is dominated by the thermal entropy and is therefore largely insensitive to entanglement along the temperature direction, EWCS displays pronounced critical scaling and provides a robust diagnostic of the quantum phase transition (QPT). We attribute this contrast to the fact that HEE at large scales is controlled by the infrared (IR) geometry, whereas EWCS is governed by deformations of the entire bulk. Our results establish EWCS as a robust probe of holographic quantum criticality in mixed states.
Abstract In this paper, we investigate the mixed-state entanglement in a model of p-wave superconductivity phase transition using holographic methods. We calculate several entanglement measures, including holographic entanglement entropy (HEE), mutual information (MI), and entanglement wedge cross-section (EWCS). Our results show that these measures display critical behavior at the phase transition points, with the EWCS exhibiting opposite temperature behavior compared to the HEE. Furthermore, we explore the behavior of thermodynamics and holographic quantum information at the zeroth-order phase transition point and find that it is opposite to that observed in the first-order phase transition. Additionally, we find that the critical exponents of all entanglement measures are twice those of the condensate. Our findings also suggest that the EWCS is a more sensitive indicator of the critical behavior of phase transitions than the HEE. Lastly, we uncover a universal inequality in the growth rates of EWCS and MI near critical points in thermal phase transitions, such as p-wave and s-wave superconductivity, suggesting that MI captures more information than EWCS when a phase transition first occurs.
A bstract We consider holographic entanglement entropy in AdS black hole backgrounds by using the limit of large number of dimensions. By dividing the geometry to two patches (with one patch covering the vicinity of the black hole horizon and another covering the other regions), we are able to obtain fully analytic expressions for the entropy when the entanglement region is a strip. We argue that apart from conformal field theories at finite temperature in high number of dimensions, our method works for nearly critical theories in 3+1 dimensions. In the case of extremal black holes, dual to quantum critical systems, the results take a particularly simple form. We also comment on the case of soliton geometries. Finally, we analyze entanglement entropy for wide strips, and propose a general formula for the first subleading term in the expansion of the entropy in (inverse) system size for generic entanglement regions.
We reveal for the first time that ultraviolet (UV) observables can diagnose quantum phase transitions (QPTs). In a class of holographic models exhibiting metal-insulator transitions, we study two types of UV observables -- high-frequency conductivity and short-range entanglement. Remarkably, we find that the derivatives of these UV observables exhibit extrema near the quantum critical point. Analytical results show these critical behaviors arise from the deformation of the asymptotic bulk geometry. Moreover, these UV diagnostics show enhanced robustness to thermal fluctuations compared to typical infrared (IR) diagnostics, providing a clean method to identify quantum criticality at finite temperature. This work opens a new window for exploring quantum critical phenomena via UV physics in the laboratory.