-Fang Li

Introduction to holographic superconductor models

In the last years it has been shown that some properties of strongly coupled superconductors can be potentially described by classical general relativity living in one higher dimension, which is known as holographic superconductors. This paper gives a quick and introductory overview of some holographic superconductor models with s-wave, p-wave and d-wave orders in the literature from point of view of bottom-up, and summarizes some basic properties of these holographic models in various regimes. The competition and coexistence of these superconductivity orders are also studied in these superconductor models.

A holographic p-wave superconductor model

A bstractWe study a holographic p-wave superconductor model in a four dimensional Einstein-Maxwell-complex vector field theory with a negative cosmological constant. The complex vector field is charged under the Maxwell field. We solve the full coupled equations of motion of the system and find black hole solutions with the vector hair. The vector hairy black hole solutions are dual to a thermal state with the U(1) symmetry as well as the spatial rotational symmetry broken spontaneously. Depending on two parameters, the mass and charge of the vector field, we find a rich phase structure: zeroth order, first order and second order phase transitions can happen in this model. We also find “retrograde condensation” in which the hairy black hole solution exists only for the temperatures above a critical value with the free energy much larger than the one of the black hole without the vector hair. We construct the phase diagram for this system in terms of the temperature and charge of the vector field.

Entanglement entropy and Wilson loop in Stückelberg holographic insulator/superconductor model

A bstractWe study the behaviors of entanglement entropy and vacuum expectation value of Wilson loop in the Stückelberg holographic insulator/superconductor model. This model has rich phase structures depending on model parameters. Both the entanglement entropy for a strip geometry and the heavy quark potential from the Wilson loop show that there exists a “confinement/deconfinement” phase transition. In addition, we find that the non-monotonic behavior of the entanglement entropy with respect to chemical potential is universal in this model. The pseudo potential from the spatial Wilson loop also has a similar non-monotonic behavior. It turns out that the entanglement entropy and Wilson loop are good probes to study the properties of the holographic superconductor phase transition.

Phase transition of holographic entanglement entropy in massive gravity

The phase structure of holographic entanglement entropy is studied in massive gravity for the quantum systems with finite and infinite volumes, which in the bulk is dual to calculating the minimal surface area for a black hole and black brane respectively. In the entanglement entropy–temperature plane, we find for both the black hole and black brane there is a Van der Waals-like phase transition as the case in thermal entropy–temperature plane. That is, there is a first order phase transition for the small charge and a second order phase transition at the critical charge. For the first order phase transition, the equal area law is checked and for the second order phase transition, the critical exponent of the heat capacity is obtained. All the results show that the phase structure of holographic entanglement entropy is the same as that of thermal entropy regardless of the volume of the spacetime on the boundary.

Van der Waals phase transition in the framework of holography

Abstract Phase structure of the quintessence Reissner–Nordstrom–AdS black hole is probed by the nonlocal observables such as holographic entanglement entropy and two point correlation function. Our result shows that, as the case of the thermal entropy, both the observables exhibit the Van der Waals-like phase transition. To reinforce this conclusion, we further check the equal area law for the first order phase transition and critical exponent of the heat capacity for the second order phase transition. We also discuss the effect of the state parameter on the phase structure of the nonlocal observables.

A holographic study on vector condensate induced by a magnetic field

A bstractWe study a holographic model with vector condensate by coupling the anti-de Sitter gravity to an Abelian gauge field and a charged vector field in (3 + 1) dimensional spacetime. In this model there exists a non-minimal coupling of the vector field to the gauge field. We find that there is a critical temperature below which the charged vector condenses via a second order phase transition. The DC conductivity becomes infinite and the AC conductivity develops a gap in the condensed phase. We study the effect of a background magnetic field on the system. It is found that the background magnetic field can induce the condensate of the vector field even in the case without chemical potential/charge density. In the case with non-vanishing charge density, the transition temperature raises with the applied magnetic field, and the condensate of the charged vector operator forms a vortex lattice structure in the spatial directions perpendicular to the magnetic field.

Competition and coexistence of order parameters in holographic multi-band superconductors

A bstractWe construct a holographic multi-band superconductor model with each complex scalar field in the bulk minimally coupled to a same gauge field. Taking into account the back reaction of matter fields on the background geometry and focusing on the two band case with two scalar order parameters, we find that depending on the strength of the back reaction and the charge ratio of the two bulk scalars, five different superconducting phases exist, and three of five phases exhibit some region where both orders coexist and are thermodynamically favored. The other two superconducting phases have only one scalar order. The model exhibits rich phase structure and we construct the full diagram for the five superconducting phases. Our analysis indicates that the equivalent attractive interaction mediated by gravity between the two order parameters tends to make the coexistence of two orders much more easy rather than more difficult.

Holographic Van der Waals-like phase transition in the Gauss–Bonnet gravity

Abstract The Van der Waals-like phase transition is observed in temperature–thermal entropy plane in spherically symmetric charged Gauss–Bonnet–AdS black hole background. In terms of AdS/CFT, the non-local observables such as holographic entanglement entropy, Wilson loop, and two point correlation function of very heavy operators in the field theory dual to spherically symmetric charged Gauss–Bonnet–AdS black hole have been investigated. All of them exhibit the Van der Waals-like phase transition for a fixed charge parameter or Gauss–Bonnet parameter in such gravity background. Further, with choosing various values of charge or Gauss–Bonnet parameter, the equal area law and the critical exponent of the heat capacity are found to be consistent with phase structures in temperature–thermal entropy plane.

Entanglement entropy in holographic p-wave superconductor/insulator model

A bstractWe continue our study of entanglement entropy in the holographic superconducting phase transitions. In this paper we consider the holographic p-wave superconductor/insulator model, where as the back reaction increases, the transition is changed from second order to first order. We find that unlike the s-wave case, there is no additional first order transition in the superconducting phase. We calculate the entanglement entropy for two strip geometries. One is parallel to the super current, and the other is orthogonal to the super current. In both cases, we find that the entanglement entropy monotonically increases with respect to the chemical potential.

Holographic thermalization and gravitational collapse in a spacetime dominated by quintessence dark energy

In this paper, the thermalization has been studied holographically. Explicitly in the gravity side, we consider the gravitational collapse of a thin shell of dust in a spacetime dominated by quintessence dark energy. With the thermalization probes such as the normalized geodesic length and minimal area surface, we study the effect of the state parameter for the quintessence dark energy on the thermalization. Our results show that the smaller the state parameter of quintessence is, the harder the plasma to thermalize. We also investigate the thermalization velocity and thermalization acceleration. We hope our results here can shed light on the nature of the quintessence dark energy.