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arXiv:2009.01529 · Physical review. D/Physical review. D.

Mixed state entanglement and thermal phase transitions

Peng Liu, Jian-Pin Wu

Published Aug 17, 2021• 15 citations
arXivHTMLPDF

Abstract

We study the relationship between mixed state entanglement and thermal phase transitions. As a typical example, we compute the holographic entanglement entropy (HEE), holographic mutual information (MI), and the holographic entanglement wedge minimum cross section (EWCS) over the superconductivity phase transition. We find that HEE, MI, and EWCS can all diagnose the superconducting phase transition. They are continuous at the critical point, but their first derivative with respect to temperature is discontinuous. MI decreases with increasing temperature and exhibits a convex behavior, while HEE increases with increasing temperature and exhibits a concave behavior. However, EWCS can exhibit either the same or the opposite behavior as MI, depending on the size of the specific configuration. These results show that EWCS captures more abundant information than HEE and MI. We also provide a new algorithm to compute the EWCS for general configurations.

DOI
10.1103/physrevd.104.046017

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We study the relationship between mixed state entanglement and thermal phase transitions. As a typical example, we compute the holographic entanglement entropy (HEE), holographic mutual information (MI), and the holographic entanglement wedge minimum cross section (EWCS) over the superconductivity phase transition. We find that HEE, MI, and EWCS can all diagnose the superconducting phase transition. They are continuous at the critical point, but their first derivative with respect to temperature is discontinuous. MI decreases with increasing temperature and exhibits a convex behavior, while HEE increases with increasing temperature and exhibits a concave behavior. However, EWCS can exhibit either the same or the opposite behavior as MI, depending on the size of the specific configuration. These results show that EWCS captures more abundant information than HEE and MI. We also provide a new algorithm to compute the EWCS for general configurations.
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.
Abstract We study the entanglement wedge cross-section (EWCS) in holographic massive gravity theory, in which a first and second-order phase transition can occur. We find that the mixed state entanglement measures, the EWCS and mutual information (MI) can characterize the phase transitions. The EWCS and MI show exactly the opposite behavior in the critical region, which suggests that the EWCS captures distinct degrees of freedom from that of the MI. More importantly, EWCS, MI and HEE all show the same scaling behavior in the critical region. We give an analytical understanding of this phenomenon. By comparing the quantum information behavior in the thermodynamic phase transition of holographic superconductors, we analyze the relationship and difference between them and provide two mechanisms of quantum information scaling behavior in the thermodynamic phase transition.
We investigate the holographic mixed-state entanglement measures in the Einstein-Maxwell-Scalar (EMS) theory. Several quantities are computed, including the holographic entanglement entropy (HEE), mutual information (MI), entanglement wedge cross-section (EWCS), and butterfly velocity (vBv_BvB​). Our findings demonstrate that these measures can effectively diagnose phase transitions. Notably, EWCS and MI, as mixed-state entanglement measures, exhibit behavior opposite to that of the HEE. Additionally, we study the butterfly velocity, a dynamic quantum information measure, and observe that it behaves differently from the static quantum information measures. We analyze the butterfly velocity and find that its non-monotonic behavior arises from the competition between two contributions in its expression, which the analytic structure suggests may be correlated with distinct physical interpretations. Moreover, we examine the scaling behavior of the holographic entanglement measures and find that all the critical exponents are equal to 111, which is twice that of the scalar field. We also explore the inequality between EWCS and MI, noting that the growth rate of MI consistently exceeds that of EWCS during phase transitions. These features are expected to be universal across thermodynamic phase transitions, with the inequalities becoming more significant as one moves away from the critical point.
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 We investigate the holographic mixed-state entanglement measures in the Einstein–Maxwell-Scalar (EMS) theory. Several quantities are computed, including the holographic entanglement entropy (HEE), mutual information (MI), entanglement wedge cross-section (EWCS), and butterfly velocity ( vBv_BvB​ v B ). Our findings demonstrate that these measures can effectively diagnose phase transitions. Notably, EWCS and MI, as mixed-state entanglement measures, exhibit behavior opposite to that of the HEE. Additionally, we study the butterfly velocity, a dynamic quantum information measure, and observe that it behaves differently from the static quantum information measures. We analyze the butterfly velocity and find that its non-monotonic behavior arises from the competition between two contributions in its expression, which the analytic structure suggests may be correlated with distinct physical interpretations. Moreover, we examine the scaling behavior of the holographic entanglement measures and find that all the critical exponents are equal to 1, which is twice that of the scalar field. We also explore the inequality between EWCS and MI, noting that the growth rate of MI consistently exceeds that of EWCS during phase transitions. These features are expected to be universal across thermodynamic phase transitions, with the inequalities becoming more significant as one moves away from the critical point.
We study mixed-state entanglement measures in Einstein-Born-Infeld (EBI) massive gravity theory, a model exhibiting both Hawking-Page phase transitions and effective metal-insulator transitions (MIT) at finite temperatures. Our comprehensive investigation reveals that the entanglement wedge cross-section (EWCS), a holographic probe of mixed-state entanglement structure, demonstrates distinctive properties in detecting phase transitions. For the effective MIT, we find that the higher-order terms of EWCS align closely with the crossover temperature, a feature not shared by holographic entanglement entropy (HEE). This sensitivity makes EWCS a complementary geometric tool for probing effective phase transitions at finite temperatures. In Hawking-Page phase transitions, we observe that all entanglement measures effectively diagnose both first-order and second-order phase transitions, with EWCS showing configuration-independent behavior. Importantly, we discover that all geometry-related quantities, including entanglement measures, demonstrate a universal critical exponent of 1/3 near the second-order phase transition point. This result suggests a fundamental connection between quantum information theory and critical phenomena in gravitational systems, and also highlights the potential of EWCS as a powerful probe for phase transitions.