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Phase structure of the quintessence Reissner-Nordstr\"{o}m-AdS black hole is probed with 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 similar Van der Waals-like phase transition. To reinforce the 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., Comment: 16 pages, 6 figures. arXiv admin note: text overlap with arXiv:1511.00383

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. We find for the case $bQ>0.5$, the phase structure is similar to that of the Reissner-Nordstr��m-AdS black hole, namely the black hole undergoes a Hawking-Page phase transition, a first order phase transition, and a second order phase transition. While for the case $bQ, 20 pages, many figures. arXiv admin note: text overlap with arXiv:1512.08855

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., Some statements about the analogy between the black hole phase transition in $T-S$ plane and Van der Waals-like phase transition in $P-V$ plane are added. This is the published version

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., 93 pages, 38 figures, 2 tables; v3: misprints corrected, published version. arXiv admin note: text overlap with arXiv:1309.5086, arXiv:1007.1981 by other authors

Gravitational collapse of a shell of charged dust surrounded by the phantom dark energy is probed by the minimal area surface, which is dual to probe the thermalization in the boundary quantum field by expectation values of Wilson loop in the framework of the AdS/CFT correspondence. We investigated mainly the effect of the phantom dark energy parameter and chemical potential on the thermalization. The result shows that the smaller the phantom dark energy parameter is, the easier the plasma thermalizes as the chemical potential is fixed, and the larger the chemical potential is, the harder the plasma thermalizes as the dark energy parameter is fixed. We get the fitting function of the thermalization curve and with it, the thermalization velocity and thermalization acceleration are discussed., Comment: arXiv admin note: text overlap with arXiv:1412.3878, arXiv:1405.5745 by other authors

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., Comment: 3 figures added, accepted by JHEP

We study in detail the phase structure of a holographic p-wave superconductor model in a five dimensional Einstein-Maxwell-complex vector field theory with a negative cosmological constant. To construct complete phase diagrams of the model, we consider both the soliton and black hole backgrounds. In both two cases, there exist second order, first order and zeroth order phase transitions, and the so-called "retrograde condensation" also happens. In particular, in the soliton case with the mass of the vector field being beyond a certain critical value, we find a series of phase transitions happen such as "insulator/superconductor/insulator/superconductor", as the chemical potential continuously increases. We construct complete phase diagrams in terms of temperature and chemical potential and find some new phase boundaries., 47 pages, 25 figures, added references, modified some figures

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 breaking 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 black hole without hair. We construct the phase diagram for this system in terms of the temperature and charge of the vector field., v3: 26 pages, 15 figures, references added, extra arguments added, to appear in JHEP

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., v2: minor changes, to appear in JHEP. arXiv admin note: text overlap with arXiv:1309.2098

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 filed 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., v3: minor changes, references added, to appear in JHEP

We study the Wilson line response in the holographic superconducting phase transitions in Gauss-Bonnet gravity. In the black brane background case, the Little-Parks periodicity is independent of the Gauss-Bonnet parameter, while in the AdS soliton case, there is no evidence for the Little-Parks periodicity. We further study the impact of the Gauss-Bonnet term on the holographic phase transitions quantitatively. The results show that such quantum corrections can effectively affect the occurrence of the phase transitions and the response to the Wilson line., 19 pages, 6 figures, 2 tables, references added

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., Comment: v2: title changed, discussions improved, references added, accepted by JHEP

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., Comment: figures added; accepted by Nuclear Physics b

We study the behaviors of entanglement entropy and vacuum expectation value of Wilson loop in the St\"{u}ckelberg 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., Comment: 23 pages,12 figures. v2: typos corrected, accepted in JHEP

In this paper we study the non-Gaussian features of the primordial fluctuations in loop quantum cosmology with the inverse volume corrections. The detailed analysis is performed in the single field slow-roll inflationary models. However, our results reflect the universal characteristics of bispectrum in loop quantum cosmology. The main corrections to the scalar bispectrum come from two aspects: one is the modifications to the standard Bunch-Davies vacuum, the other is the corrections to the background dependent variables, such as slow-roll parameters. Our calculations show that the loop quantum corrections make $f_{{\rm NL}}$ of the inflationary models increase 0.1%. Moreover, we find that two new shapes arise, namely $\mathcal F_{1}$ and $\mathcal F_{2}$. The former gives a unique loop quantum feature which is less correlated with the local, equilateral and single types, while the latter is highly correlated with the local one., Comment: matched to the published version. 30 pages, 4 figures