Holographic Phase Transition Research Articles

Holographic p-wave superconductor with high-order derivative correction

In the probe limit, we numerically study the holographic p-wave superconductor phase transition in the high-order derivative theory. Concretely, we study the influences of the high-order derivative correction term αRF2 on the Maxwell complex vector model (MCV) in the five-dimensional AdS black hole and soliton backgrounds, respectively. In the black hole background, the improving correction parameter α increases the critical temperature and thus enhances the conductor/superconductor phase transition. Meanwhile, as the RF2 correction becomes stronger, the ratio of the energy gap to the critical temperature decreases from 9.858 to 5.995, which obviously deviates from the universal value. In the soliton background, we find that the correction does not affect the critical chemical potential. However, as the correction parameter α increases, the vector condensate grows faster, which might suggest that the improving α enhances the insulator/superconductor in some sense. The location of the second pole of imaginary part of conductivity increases with α, which implies that the energy of the quasiparticle excitation increases with the improving correction. In addition, the effects of α on the superfluid density agree with the one on the critical value as well as the condensate in both models. Furthermore, the critical exponent of condensate and superfluid density near the critical point is always 1/2 and 1, respectively.

Phase transitions in 3D gravity and fractal dimension

We show that for three dimensional gravity with higher genus boundary conditions, if the theory possesses a sufficiently light scalar, there is a second order phase transition where the scalar field condenses. This three dimensional version of the holographic superconducting phase transition occurs even though the pure gravity solutions are locally AdS3. This is in addition to the first order Hawking-Page-like phase transitions between different locally AdS3 handlebodies. This implies that the Rényi entropies of holographic CFTs will undergo phase transitions as the Rényi parameter is varied, as long as the theory possesses a scalar operator which is lighter than a certain critical dimension. We show that this critical dimension has an elegant mathematical interpretation as the Hausdorff dimension of the limit set of a quotient group of AdS3, and use this to compute it, analytically near the boundary of moduli space and numerically in the interior of moduli space. We compare this to a CFT computation generalizing recent work of Belin, Keller and Zadeh, bounding the critical dimension using higher genus conformal blocks, and find a surprisingly good match.

Holographic insulator/superconductor transition with exponential nonlinear electrodynamics probed by entanglement entropy

From the viewpoint of holography, we study the behaviors of the entanglement entropy in insulator/superconductor transition with exponential nonlinear electrodynamics (ENE). We find that the entanglement entropy is a good probe to the properties of the holographic phase transition. Both in the half space and the belt space, the non-monotonic behavior of the entanglement entropy in superconducting phase versus the chemical potential is general in this model. Furthermore, the behavior of the entanglement entropy for the strip geometry shows that the confinement/deconfinement phase transition appears in both insulator and superconductor phases. And the critical width of the confinement/deconfinement phase transition depends on the chemical potential and the exponential coupling term. More interestingly, the behaviors of the entanglement entropy in their corresponding insulator phases are independent of the exponential coupling factor but depends on the width of the subsystem mathcal {A}.

Subregion holographic complexity and renormalization group flows

We investigate subregion holographic complexity in the context of renormalization group flow geometries. We use both the Poinca\'re slicing and the Janus ansatz as holographic duals to renormalization group flows in the boundary conformal field theory. In the former metric, subregion complexity is computed for a disc and a strip shaped entangling region. For the disc shaped region, consistent emergence of length scales for flow to the deep infra-red is established. For strip shaped regions, we find that complexity cannot locate holographic phase transitions in a sharp domain wall scenario. For smooth domain walls, we find that the complexity might be an indicator of such phase transitions, and give numerical evidence that its derivative changes sign across a transition. Finally, the complexity is computed numerically using the Janus ansatz.

A smeared quantum phase transition in disordered holography

We study the effects of quenched one-dimensional disorder on the holographic Weyl semimetal quantum phase transition (QPT), with a particular focus on the quantum critical region. We observe the smearing of the sharp QPT linked to the appearance of rare regions at the horizon where locally the order parameter is non-zero. We discuss the role of the disorder correlation and we compare our results to expectations from condensed matter theory at weak coupling. We analyze also the interplay of finite temperature and disorder. Within the quantum critical region we find indications for the presence of log-oscillatory structures in the order parameter hinting at the existence of an IR fixed point with discrete scale invariance.

Wilson loop's phase transition probed by non-local observable

In order to give further insights into the holographic Van der Waals phase transition, it would be of great interest to investigate the behavior of Wilson loop across the holographic phase transition for a higher dimensional hairy black hole. We offer a possibility to proceed with a numerical calculation in order to discussion on the hairy black hole's phase transition, and show that Wilson loop can serve as a probe to detect a phase structure of the black hole. Furthermore, for a first order phase transition, we calculate numerically the Maxwell's equal area construction; and for a second order phase transition, we also study the critical exponent in order to characterize the Wilson loop's phase transition.

Holographic Phase Transition in AdS Spacetime with Global Monopole

With motivation by holography, in this paper we attempt to survey whether holographic Van der Waals phase transition can be observed in the Anti-de Sitter spacetime with global monopole. We offer a possibility to proceed with a numerical calculation in order to discussion on phase transition. Furthermore, we verify numerically the Maxwell’s equal area construction. In addition, the effect of global monopole on phase transition is also presented.

Holographic Van der Waals phase transition of the higher-dimensional electrically charged hairy black hole

With motivation by holography, employing black hole entropy, two-point connection function and entanglement entropy, we show that, for the higher-dimensional Anti-de Sitter charged hairy black hole in the fixed charged ensemble, a Van der Waals-like phase transition can be observed. Furthermore, based on the Maxwell equal-area construction, we check numerically the equal-area law for a first order phase transition in order to further characterize the Van der Waals-like phase transition.

Real-Time Dynamics and Phase Separation in a Holographic First-Order Phase Transition.

We study the fully nonlinear time evolution of a holographic system possessing a first order phase transition. The initial state is chosen in the spinodal region of the phase diagram, and it includes an inhomogeneous perturbation in one of the field theory directions. The final state of the time evolution shows a clear phase separation in the form of domain formation. The results indicate the existence of a very rich class of inhomogeneous black hole solutions.

Holographic cosmology and phase transitions of SYM theory

We study the time development of strongly coupled ${\cal N}=4$ supersymmetric Yang Mills (SYM) theory on cosmological Friedmann-Robertson-Walker (FRW) backgrounds via the AdS/CFT correspondence. We implement the cosmological background as a boundary metric fulfilling the Friedmann equation with a four-dimensional cosmological constant and a dark radiation term. We analyze the dual bulk solution of the type IIB supergravity and find that the time-dependence of the FRW background strongly influences the dynamical properties of the SYM theory. We in particular find a phase transition between a confined and a deconfined phase. We also argue that some cosmological solutions could be related to the inflationary scenario.

Holographic phase transition for a black hole in the background with dark energy

In the background with dark energy, we investigate the phase structure of thermodynamic entropy and entanglement entropy. We investigate respectively the effect of the charge and state parameters of the dark energy on the phase structure of the black hole. For a fixed state parameter of dark energy, as the value of the charge increases, the phase structures of the thermodynamical entropy and the entanglement entropy are similar as that of the Van der Waals phase transition. That is, the black hole undergoes the first order phase transition and second order phase transition successively and reaches to a stable state at last. For a fixed charge, as the state parameter of dark energy increases, the phase structures of the thermodynamical entropy is not similar to the entanglement entropy. Especially, the tendency of the change of entanglement entropy with respect to the state parameter is opposite to the thermodynamic entropy. The same is that the black hole undergoes the first order phase transition and second order phase transition successively as the state parameter of dark energy increases. For the thermodynamics entropy and entanglement entropy, we find Maxwells equal area law holds for the unstable region of the first order phase transition, and the critical exponent of the heat capacity is 2/3 near the critical points of the second order phase transition.

A general holographic insulator/superconductor model with dark matter sector away from the probe limit

We investigate holographic phase transitions with dark matter sector in the AdS soliton background away from the probe limit. In cases of weak backreaction, we find that the larger coupling parameter α makes the gap of condensation shallower and the critical chemical potential keeps as a constant. In contrast, for very heavy backreaction, the dark matter sector could affect the critical chemical potential and the order of phase transitions. We also find the jump of the holographic topological entanglement entropy corresponds to a first order transition between superconducting states in this model with dark matter sector. More importantly, for certain sets of parameters, we observe novel phenomenon of retrograde condensation. In a word, the dark matter sector provides richer physics in the phase structure and the holographic superconductor properties are helpful in understanding dark matter.

Holographic entanglement entropy in metal/superconductor phase transition with exponential nonlinear electrodynamics

We study the holographic entanglement entropy in metal/superconductor phase transition with exponential nonlinear electrodynamics (ENE) in four and five dimensional spacetimes. We find that the holographic entanglement entropy is powerful tool in studying the properties of the holographic phase transition. For the operator $\langle\mathcal{O}_{+}\rangle$, we observe that the entanglement entropy in 4-dimensional spacetime decreases in metal phase but changes non-monotonously in superconducting phase with the increase of the ENE parameter. Interestingly, the change of the entanglement entropy in 5-dimensional spacetime for both the phases is monotonous as the ENE factor alters. For the operator $\langle\mathcal{O}_{-}\rangle$, we show that the behavior of entanglement entropy in four and five dimensions changes monotonously for both phases as one tunes the strength of the ENE. Furthermore, for both the operators the entanglement entropy in four or five dimensional black hole increases with the increase of the width of the region.

Lifshitz scaling effects on the holographic paramagnetism-ferromagnetism phase transition

In the probe limit, we investigate holographic paramagnetism-ferromagnetism phase transition in the four-dimensional (4D) and five-dimensional(5D) Lifshitz black holes by means of numerical and semi-analytical methods, which is realized by introducing a massive 2-form field coupled to the Maxwell field. We find that the Lifshitz dynamical exponent $z$ contributes evidently to magnetic moment and hysteresis loop of single magnetic domain quantitatively not qualitatively. Concretely, in the case without external magnetic field, the spontaneous magnetization and ferromagnetic phase transition happen when the temperature gets low enough, and the critical exponent for the magnetic moment is always $1/2$, which is in agreement with the result from mean field theory. And the increasing $z$ enhances the phase transition and increases the DC resistivity which behaves as the colossal magnetic resistance effect in some materials. Furthermore, in the presence of the external magnetic field, the magnetic susceptibility satisfies the Cure-Weiss law with a general $z$. But the increase of $z$ will result in shortening the period of the external magnetic field.

Lifshitz holographic superconductor in Hořava–Lifshitz gravity

We study the holographic phase transition of superconductor dual to a Lifshitz black brane probed by an anisotropic scalar field in the probe limit in Ho\u{r}ava-Lifshitz gravity. With the use of numerical and analytical method, we investigate how the critical temperature of the condensation is affected by the Lifshitz exponent $z$, $\alpha-$correction term in the action as well as the dimensions of the gravity. We also numerically explore the condensation of the dual operator and optical conductivity of the holographic system. Various interesting properties of the holographic condensation affected by the parameters of model are discussed.

Analytical study on holographic superfluid in AdS soliton background

We analytically study the holographic superfluid phase transition in the AdS soliton background by using the variational method for the Sturm-Liouville eigenvalue problem. By investigating the holographic s-wave and p-wave superfluid models in the probe limit, we observe that the spatial component of the gauge field will hinder the phase transition. Moreover, we note that, different from the AdS black hole spacetime, in the AdS soliton background the holographic superfluid phase transition always belongs to the second order and the critical exponent of the system takes the mean-field value in both s-wave and p-wave models. Our analytical results are found to be in good agreement with the numerical findings.

Holographic vector superconductor in Gauss–Bonnet gravity

In the probe limit, we numerically study the holographic p-wave superconductor phase transitions in the higher curvature theory. Concretely, we study the influences of Gauss–Bonnet parameter α on the Maxwell complex vector model (MCV) in the five-dimensional Gauss–Bonnet–AdS black hole and soliton backgrounds, respectively. In the two backgrounds, the improving Gauss–Bonnet parameter α and dimension of the vector operator Δ inhibit the vector condensate. In the black hole, the condensate quickly saturates a stable value at lower temperature. Moreover, both the stable value of condensate and the ratio ωg/Tc increase with α. In the soliton, the location of the second pole of the imaginary part increases with α, which implies that the energy of the quasiparticle excitation increases with the improving higher curvature correction. In addition, the influences of the Gauss–Bonnet correction on the MCV model are similar to the ones on the SU(2) p-wave model, which confirms that the MCV model is a generalization of the SU(2) Yang–Mills model even without the applied magnetic field to some extent.

Holographic Phase Transition Probed by Nonlocal Observables

From the viewpoint of holography, the phase structure of a 5-dimensional Reissner-Nordström-AdS black hole is probed by the two-point correlation function, Wilson loop, and entanglement entropy. As the case of thermal entropy, we find for all the probes that the black hole undergoes a Hawking-Page phase transition, a first-order phase transition, and a second-order phase transition successively before it reaches a stable phase. In addition, for these probes, we find that the equal area law for the first-order phase transition is valid always and the critical exponent of the heat capacity for the second-order phase transition coincides with that of the mean field theory regardless of the size of the boundary region.

Massive 2-form field and holographic ferromagnetic phase transition

In this paper, we investigate in some detail the holographic ferromagnetic phase transition in an AdS${_4}$ black brane background by introducing a massive 2-form field coupled to the Maxwell field strength in the bulk. In the two probe limits, one is to neglect the back reaction of the 2-form field to the background geometry and to the Maxwell field, and the other to neglect the back reaction of both the Maxwell field and the 2-form field, we find that the spontaneous magnetization and the ferromagnetic phase transition always happen when the temperature gets low enough with similar critical behavior. We calculate the DC resistivity in a semi-analytical method in the second probe limit and find it behaves as the colossal magnetic resistance effect in some materials. In the case with the first probe limit, we obtain the off-shell free energy of the holographic model near the critical temperature and compare with the Ising-like model. We also study the back reaction effect and find that the phase transition is always second order. In addition, we find an analytical Reissner-Norstr\"om-like black brane solution in the Einstein-Maxwell-2-form field theory with a negative cosmological constant.

Fermionic phase transition induced by the effective impurity in holography

We investigate the holographic fermionic phase transition induced by the effective impurity in holography, which is introduced by massless scalar fields in Einstein-Maxwell-massless scalar gravity. We obtain a phase diagram in $(\alpha, T)$ plane separating the Fermi liquid phase and the non-Fermi liquid phase.