All Results

Phase structure of the Born-Infeld-anti-de Sitter black holes probed by non-local observables

Zeng, Xiao-Xiong; Liu, Xian-Ming; Li, Li-FangSubjects: Geosciences >> Space Physics

With the non-local observables such as two point correlation function and holographic entanglement entropy, we probe the phase structure of the Born-Infeld-anti-de Sitter black holes. For the case bQ > 0.5, where b is the Born-Infeld parameter and Q is the charge of the black hole, the phase structure is found to be similar to that of the Van der Waals phase transition, namely the black hole undergoes a first order phase transition and a second order phase transition before it reaches a stable phase. While for the case bQ < 0.5, a new phase branch emerges besides the Van der Waals phase transition. 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 these results are found to be the same as that observed in the entropy-temperature plane. |

A holographic study on vector condensate induced by a magnetic field

Cai, Rong-Gen; He, Song; Li, Li; Li, Li-FangSubjects: Geosciences >> Space Physics

We 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. |

Vector condensate and AdS soliton instability induced by a magnetic field

Cai, Rong-Gen; Li, Li; Li, Li-Fang; Wu, YouSubjects: Geosciences >> Space Physics

We continue to study the holographic p-wave superconductor model in the Einstein-Maxwell-complex vector field theory with a non-minimal coupling between the complex vector field and the Maxwell field. In this paper we work in the AdS soliton background which describes a conformal field theory in the confined phase and focus on the probe approximation. We find that an applied magnetic field can lead to the condensate of the vector field and the AdS soliton instability. As a result, a vortex lattice structure forms in the spatial directions perpendicular to the applied magnetic field. As a comparison, we also discuss the vector condensate in the Einstein-SU(2) Yang-Mills theory and find that in the setup of the present paper, the Einstein-Maxwell-complex vector field model is a generalization of the SU(2) model in the sense that the vector field has a general mass and gyromagnetic ratio. |

Competition between s-wave order and d-wave order in holographic superconductors

Li, Li-Fang; Cai, Rong-Gen; Li, Li; Wang, Yong-QiangSubjects: Geosciences >> Space Physics

We study competition between s-wave order and d-wave order through two holographic superconductor models. We find that once the coexisting phase appears, it is always thermodynamically favored, and that the coexistence phase is narrow and one condensate tends to kill the other. The phase diagram is constructed for each model in terms of temperature and the ratio of charges of two orders. We further compare the behaviors of some thermodynamic quantities, and discuss the different aspects and identical ones between two models. |

Entanglement entropy in a holographic p-wave superconductor model

Li, Li-Fang; Cai, Rong-Gen; Li, Li; Shen, ChaoSubjects: Geosciences >> Space Physics

In a recent paper, arXiv:1309.4877, a holographic p-wave model has been proposed in an Einstein Maxwell-complex vector field theory with a negative cosmological constant. The model exhibits rich phase structure depending on the mass and the charge of the vector field. We investigate the behavior of the entanglement entropy of dual field theory in this model. When the above two model parameters change, we observe the second order, first order and zeroth order phase transitions from the behavior of the entanglement entropy at some intermediate temperatures. These imply that the entanglement entropy can indicate not only the occurrence of the phase transition, but also the order of the phase transition. The entanglement entropy is indeed a good probe to phase transition. Furthermore, the "retrograde condensation" which is a sub-dominated phase is also reflected on the entanglement entropy. (C) 2015 The Authors. Published by Elsevier B.V. |

Vector condensate and AdS soliton instability induced by a magnetic field

Cai, Rong-Gen; Li, Li; Li, Li-Fang; Wu, YouSubjects: Physics >> The Physics of Elementary Particles and Fields

We continue to study the holographic p-wave superconductor model in the Einstein-Maxwell-complex vector field theory with a non-minimal coupling between the complex vector field and the Maxwell field. In this paper we work in the AdS soliton background which describes a conformal field theory in the confined phase and focus on the probe approximation. We find that an applied magnetic field can lead to the condensate of the vector field and the AdS soliton instability. As a result, a vortex lattice structure forms in the spatial directions perpendicular to the applied magnetic field. As a comparison, we also discuss the vector condensate in the Einstein-SU(2) Yang-Mills theory and find that in the setup of the present paper, the Einstein-Maxwell-complex vector field model is a generalization of the SU(2) model in the sense that the vector field has a general mass and gyromagnetic ratio. |

A holographic p-wave superconductor model

Cai, Rong-Gen; Li, Li; Li, Li-FangSubjects: Physics >> The Physics of Elementary Particles and Fields

We 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. |

A holographic study on vector condensate induced by a magnetic field

Cai, Rong-Gen; He, Song; Li, Li; Li, Li-FangSubjects: Physics >> The Physics of Elementary Particles and Fields

We 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

Cai, Rong-Gen; Li, Li; Li, Li-Fang; Wang, Yong-Qiang;Subjects: Physics >> The Physics of Elementary Particles and Fields

We 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. |

Entanglement entropy in holographic p-wave superconductor/insulator model

Cai, Rong-Gen; Li, Li; Li, Li-Fang; Su, Ru-Keng;Subjects: Physics >> The Physics of Elementary Particles and Fields

We 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. |