Lifshitz Black Hole Background Research Articles

Topological invariants of the Ryu-Takayanagi (RT) surface used to observe holographic superconductor phase transition

We study the phase transitions in the metal/superconductor system using topological invariants of the Ryu-Takayanagi (RT) surface and the volume enclosed by the RT surface in the Lifshitz black hole background. It is shown that these topological invariant quantities identify not only the phase transition but also its order. According to these findings a discontinuity slope is observed at the critical points for these invariant quantities that correspond to the second order of phase transition. These topological invariants provide a clearer illustration of the superconductor phase transition than do the holographic entanglement entropy and the holographic complexity. Also, the backreaction parameter, k, is found to have an important role in distinguishing the critical points. The reducing values of the parameter k means that the backreaction of the matter fields are negligible. A continuous slope is observed around the critical points which is characteristic of the probe limit. In addition, exploring the nonlinear electrodynamic, the effects of the nonlinear parameter, β, is investigated. Finally the properties of conductivity are numerically explored in our model.

Holographic p-wave superconductor in Lifshitz gravity with RF2 correction

In the probe limit, we numerically construct the holographic p-wave superconductor model in the Lifshitz gravity with the high-order derivative correction. Concretely, we study the effects of both Lifshitz scaling and the RF2 correction on the Maxwell-complex-vector model in the five-dimensional Lifshitz black hole and soliton backgrounds, respectively. We find that the increasing Lifshitz parameter u inhibits the conductor/superconductor phase transition and suppresses the frequency dependent conductivity. For the coexistence of both Lifshitz parameter and RF2 correction, the larger Lifshitz parameter u suppresses the effect of RF2 correction on the superconductor model. Moreover, the Lifshitz parameter inhibits the insulator/superconductor phase transition at first, and then enhances the phase transition when the value of Lifshitz parameter is large enough. Meanwhile, the larger parameter u enlarges the energy of quasiparticle excitation. Near the critical point, both systems undergo a second-order phase transition, which is upheld by the comparison of grand potential between normal state and condensate state.

Exponential nonlinear electrodynamics and backreaction effects on holographic superconductor in the Lifshitz black hole background

We analytically describe the properties of the s-wave holographic superconductor with the exponential nonlinear electrodynamics in the Lifshitz black hole background in four-dimensions. Employing an assumption the scalar and gauge fields backreact on the background geometry, we calculate the critical temperature as well as the condensation operator. Based on Sturm–Liouville method, we show that the critical temperature decreases with increasing exponential nonlinear electrodynamics and Lifshitz dynamical exponent, [Formula: see text], indicating that condensation becomes difficult. Also we find that the effects of backreaction has a more important role on the critical temperature and condensation operator in small values of Lifshitz dynamical exponent, while [Formula: see text] is around one. In addition, the properties of the upper critical magnetic field in Lifshitz black hole background using Sturm–Liouville approach is investigated to describe the phase diagram of the corresponding holographic superconductor in the probe limit. We observe that the critical magnetic field decreases with increasing Lifshitz dynamical exponent, [Formula: see text], and it goes to zero at critical temperature, independent of the Lifshitz dynamical exponent, [Formula: see text].

Correlation functions in theories with Lifshitz scaling

The 2+1 dimensional quantum Lifshitz model can be generalised to a class of higher dimensional free field theories that exhibit Lifshitz scaling. When the dynamical critical exponent equals the number of spatial dimensions, equal time correlation functions of scaling operators in the generalised quantum Lifshitz model are given by a d-dimensional higher-derivative conformal field theory. Autocorrelation functions in the generalised quantum Lifshitz model in any number of dimensions can on the other hand be expressed in terms of autocorrelation functions of a two-dimensional conformal field theory. This also holds for autocorrelation functions in a strongly coupled Lifshitz field theory with a holographic dual of Einstein-Maxwell-dilaton type. The map to a two-dimensional conformal field theory extends to autocorrelation functions in thermal states and out-of-equilbrium states preserving symmetry under spatial translations and rotations in both types of Lifshitz models. Furthermore, the spectrum of quasinormal modes of scalar field perturbations in Lifshitz black hole backgrounds can be obtained analytically at low spatial momenta and exhibits a linear dispersion relation at z = d. At high momentum, the mode spectrum can be obtained in a WKB approximation and displays very different behaviour compared to holographic duals of conformal field theories. This has implications for thermalisation in strongly coupled Lifshitz field theories with z > 1.

Weyl holographic superconductor in the Lifshitz black hole background

We investigate analytically the properties of the Weyl holographic superconductor in the Lifshitz black hole background. We find that the critical temperature of the Weyl superconductor decreases with increasing Lifshitz dynamical exponent, $z$, indicating that condensation becomes difficult. In addition, it is found that the critical temperature and condensation operator could be affected by applying the Weyl coupling, $\gamma$. Moreover, we compute the critical magnetic field and investigate its dependence on the parameters $\gamma$ and $z$. Finally, we show numerically that the Weyl coupling parameter $\gamma$ and the Lifshitz dynamical exponent $z$ together control the size and strength of the conductivity peak and the ratio of gap frequency over critical temperature $\omega_{g}/T_{c}$.

Lifshitz scaling effects on holographic superconductors

Via numerical and analytical methods, the effects of the Lifshitz dynamical exponent z on the holographic superconductor models are studied in some detail, including s-wave and p-wave models. Working in the probe limit, we calculate the condensation and conductivity in both Lifshitz black hole and soliton backgrounds with a general z. For both the s-wave and p-wave models in the black hole backgrounds, as z increases, the phase transition becomes difficult and the conductivity is suppressed. For the Lifshitz soliton background, when z increases, the critical chemical potential increases in both the s-wave model (with a fixed mass of the scalar field) and p-wave model. For the p-wave model in both the Lifshitz black hole and soliton backgrounds, the anisotropy between the AC conductivity in different spatial directions is suppressed when z increases. In all cases, we find that the critical exponent of the condensation is always 1/2, independent of z and spacetime dimension. The analytical results from the Sturm–Liouville variational method uphold the numerical calculations. The implications of these results are discussed.

Holographic approach to nonequilibrium dynamics of moving mirrors coupled to quantum critical theories

We employ the holographic method to study fluctuations and dissipation of an $n$-dimensional moving mirror coupled to quantum critical theories in $d$ spacetime dimensions. The bulk counterpart of the mirror with perfect reflection is a D$(n+1)$ brane in the Lifshitz geometry of $d+1$ dimensions. The motion of the mirror can be realized from the dynamics of the brane at the boundary of the bulk. The excited modes of the brane in the bulk render the mirror undergoing Brownian motion. For small displacement of the mirror, we derive the analytical results of the correlation functions and response functions. The dynamics of the mirror due to small fluctuations around the brane vacuum state in the bulk is found supraohmic so that after initial growth, the velocity fluctuations approach a saturated value at late time with a power-law behavior. On the contrary, in the Lifshitz black hole background, the mirror in thermal fluctuations shows that its relaxation dynamics becomes ohmic, and the saturation of velocity fluctuations is reached exponentially in time. Finally a comparison is made with the result of a moving mirror driven by free fields.

Generalized superconductors and holographic optics

We study generalized holographic s-wave superconductors in four dimensional R-charged black hole and Lifshitz black hole backgrounds, in the probe limit. We first establish the superconducting nature of the boundary theories, and then study their optical properties. Numerical analysis indicates that a negative Depine-Lakhtakia index may appear at low frequencies in the theory dual to the R-charged black hole, for certain temperature ranges, for specific values of the charge parameter. The corresponding cut-off values for these are numerically established in several cases. Such effects are seen to be absent in the Lifshitz background where this index is always positive.

Lifshitz holography with a probe Yang–Mills field

Taking as a probe an SU(2) gauge field with Yang–Mills action in a 3+1 dimensional Lifshitz black hole background, we use the gauge/gravity correspondence to discuss finite temperature effects in the dual theory defined on the boundary. In order to test the dependence of results on the anisotropic scaling exponent z we consider two analytical black hole solutions with z=2 and z=4. Apart from solving the equations of motion in the bulk using a numerical approach, we also apply an analytical approximation allowing the determination of the phase transition character, the critical exponent and the critical temperature behavior as a function of z.

Scalar field scattering by a Lifshitz black hole under a nonminimal coupling

We study the behavior of a scalar field under a z = 3 Lifshitz black hole background, in a way that is non-minimally coupled to the gravitational field. A general analytical solution is obtained along with two sets of quasinormal modes associated to different boundary conditions that can be imposed on the scalar field, non-minimal coupling parameter appears explicitly on these solutions. Stability of quasinormal modes can be studied and ensured for both cases. Also, the reflection and absorption coefficients are calculated, as well as the absorption cross section which features an interesting behavior because of being attenuated by terms strongly dependant on the non-minimal coupling. By a suitable change of variables a soliton solution can also be obtained and the stability of the quasinormal modes are studied and ensured.

Holographic charge transport in Lifshitz black hole backgrounds

We study charge transport properties in a domain-wall geometry, whose near horizon IR geometry is a Lifshitz black hole and whose UV geometry is AdS. The action for the gauge field contains the standard Maxwell term plus the Weyl tensor coupled to Maxwell field strengths. In four dimensions we calculate the conductivity via both the membrane paradigm and Kubo’s formula. Precise agreements between both methods are obtained. Moreover, we perform an analysis of the four-dimensional electro-magnetic duality in our domain-wall background and find that the relation between the longitudinal and transverse components of the current-current correlation functions and those of the ‘dual’ counterparts holds, irrespective of the near horizon IR geometry. Conductivity at extremality is also investigated. Generalizations to higher dimensions are performed.