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arXiv:2209.12421 · The European Physical Journal C

Holographic entanglement entropy and complexity for D-wave superconductors

Yuanceng Xu, Yu Shi, Dong Wang, Qiyuan Pan

Published Mar 8, 2023• 6 citations
arXivHTMLPDF

Abstract

Abstract Using the RT formula and the subregion CV conjecture, we numerically investigate the holographic entanglement entropy (HEE) and holographic subregion complexity (HSC) for two holographic d-wave superconducting models with backreactions. We find that the HEE and HSC can probe these two d-wave superconducting phase transitions. The HEE of the superconducting phase is always lower than that of the normal phase. For the HSC, however, it behaves differently and interestingly, which depends on both the strip-width $$L_{x}$$ L x and backreaction $$\kappa $$ κ . More specifically, when the backreaction is larger than a particular critical value, or the strip-width of the boundary subsystem is smaller than a particular critical value, the HSC in the superconducting phase is larger than that in the normal phase, and vice versa.

DOI
10.1140/epjc/s10052-023-11327-y

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Abstract Using the RT formula and the subregion CV conjecture, we numerically investigate the holographic entanglement entropy (HEE) and holographic subregion complexity (HSC) for two holographic d-wave superconducting models with backreactions. We find that the HEE and HSC can probe these two d-wave superconducting phase transitions. The HEE of the superconducting phase is always lower than that of the normal phase. For the HSC, however, it behaves differently and interestingly, which depends on both the strip-width LxL_{x}Lx​ L x and backreaction κ\kappa κ κ . More specifically, when the backreaction is larger than a particular critical value, or the strip-width of the boundary subsystem is smaller than a particular critical value, the HSC in the superconducting phase is larger than that in the normal phase, and vice versa.
We examine the behavior of entanglement entropy S EE of a subsystem A in a fully backreacted holographic model of a 1 + 1 dimensional p wave superconductor across the phase transition. For a given temperature, the system goes to a superconducting phase beyond a critical value of the charge density. The entanglement entropy, considered as a function of the charge density at a given temperature, has a cusp at the critical point. In addition, we find that there are three different behaviors in the condensed phase, depending on the subsystem size. For a subsystem size l smaller than a critical size l c1, S EE continues to increase as a function of the charge density as we cross the phase transition. When l lies between l c1 and another critical size l c2 the entanglement entropy displays a non-monotonic behavior, while for l > l c2 it decreases monotonically. At large charge densities S EE appears to saturate. The non-monotonic behavior leads to a novel phase diagram for this system.
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.
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.
In this paper, we investigate the holographic phase transition with dark matter sector in the AdS black hole background away from the probe limit. We discuss the properties of phases mostly from the holographic topological entanglement entropy of the system. We find the entanglement entropy is a good probe to the critical temperature and the order of the phase transition in the general model. The behaviors of entanglement entropy at large strip size suggest that the area law still holds when including dark matter sector. We also conclude that the holographic topological entanglement entropy is useful in detecting the stability of the phase transitions. Furthermore, we derive the complete diagram of the effects of coupled parameters on the critical temperature through the entanglement entropy and analytical methods.
In this paper, we holographically quantify the entanglement and complexity for mixed states by following the prescription of purification. The bulk theory we consider in this work is a hyperscaling violating solution, characterized by two parameters, hyperscaling violating exponent $\ensuremath{\theta}$ and dynamical exponent zzz. This geometry is due to a nonrelativistic strongly coupled theory with hidden Fermi surfaces. We first compute the holographic analogy of entanglement of purification, denoted as the minimal area of the entanglement wedge cross section and observe the effects of zzz and $\ensuremath{\theta}$. Then in order to probe the mixed state complexity we compute the mutual complexity for the Banados Teitelboim Zanelli (BTZ) black hole and the hyperscaling violating geometry by incorporating the holographic subregion complexity conjecture. We carry this out for two disjoint subsystems separated by a distance and also when the subsystems are adjacent with subsystems making up the full system. Furthermore, various aspects of holographic entanglement entropy such as the entanglement Smarr relation, the Fisher information metric, and the butterfly velocity have also been discussed.
We study various entanglement measures associated with certain nonconformal field theories. We consider nonconformal Dp\mathrm{D}pDp-brane backgrounds, which are dual to these field theories, for our holographic analysis. Restricting our interests in p=1p=1p=1, 2, 4, we explicitly compute properties of holographic entanglement entropy and the entanglement wedge cross section, EW{\mathrm{E}}_{W}EW​, corresponding to two parallel strip shaped boundary subregions in these setups. We study low and high temperature behaviors of these quantities analytically as well as by using numerical methods. In all cases, the EW{\mathrm{E}}_{W}EW​ decreases monotonically with temperature. We observe discontinuous jumps in EW{\mathrm{E}}_{W}EW​, while the width of (as well as the separation between) the subregions reaches critical values in all the cases considered. However, the corresponding holographic mutual information IM{\mathtt{I}}_{M}IM​ continuously decreases to zero for the aforementioned configurations. We also notice that the conjectured inequality ${\mathrm{E}}_{W}\ensuremath{\ge}{\mathtt{I}}_{M}/2$ still holds for nonconformal field theories as well. We analytically determine the critical separation between these subregions that triggers a phase transition in the holographic mutual information.