Lifshitz Dynamical Exponent Research Articles

Informational properties of holographic Lifshitz field theory * *Supported by the Natural Science Foundation of China (11775036, 11905083, 11847055, 11705161) and Fok Ying Tung Education Foundation (171006). Guoyang Fu is supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX20_2973). Top Talent Support Program from Yangzhou University

In this paper, we explore the properties of holographic entanglement entropy (HEE), mutual information (MI) and entanglement of purification (EoP) in holographic Lifshitz theory. These informational quantities exhibit some universal properties of holographic dual field theory. For most configuration parameters and temperatures, these informational quantities change monotonically with the Lifshitz dynamical critical exponent z. However, we also observe some non-monotonic behaviors for these informational quantities in some specific spaces of configuration parameters and temperatures. A particularly interesting phenomenon is that a dome-shaped diagram emerges in the behavior of MI vs z, and correspondingly a trapezoid-shaped profile appears in that of EoP vs z. This means that for some specific configuration parameters and temperatures, the system measured in terms of MI and EoP is entangled only in a certain intermediate range of z.

Chaotic dynamics of string around charged black brane with hyperscaling violation

By fast Lyapunov indicator (FLI), we study the chaotic dynamics of closed string around charged black brane with hyperscaling violation (HV). The Hawking temperature, Lifshitz dynamical exponent and HV exponent together affect the chaotic dynamics of this system. The temperature plays the role of driving the closed string to escape to infinity. There is a threshold value z∗ = 2, below which the string is captured by the black brane no matter where the string is placed at the beginning. However, when z > 2, the string escapes to infinity if it is placed near the black brane at the beginning, but if the initial position of string is far away from the black brane, it oscillates around the black brane till eternity, which is a quasi-periodic motion. HV exponent plays the role of driving the string falling into the black brane. With the increase of HV exponent θ, the falling velocity becomes faster. We find that when we heat the system with large HV exponent, the chaotic system does not essentially changes. It indicates that the HV exponent plays a very important role in determining the state of the chaotic system. Also we study the effect from the winding number of the string. The study indicates that the chaotic dynamics of the string is insensitive to the winding number.

Optical properties of Born–Infeld-dilaton-Lifshitz holographic superconductors

In this letter, we first study the Lifshitz-dilaton holographic superconductors with nonlinear Born–Infeld (BI) gauge field and obtain the critical temperature of the system for different values of Lifshitz dynamical exponent, z, and nonlinear parameter b. We find that for fixed value of b, the critical temperature decreases with increasing z. This indicates that the increase of anisotropy between space and time (encoded in Lifshitz exponent z) prevents the phase transition. Also, for fixed value of z, the critical temperature decrease with increasing b. Then, we investigate the optical properties of (2+1) and (3+1)-dimensional BI-Lifshitz holographic superconductors in the presence of dilaton field. We explore the refractive index of the system. This is an important study, since it discloses the effects of anisotropy between space and time as well as nonlinearity of electrodynamics model and dimension on strange metamaterial behavior of the holographic superconductor. For z=1 and (2+1)-dimensional holographic superconductor, we observe negative real part for permittivity Re[ϵ] as frequency ω decreases. Thus, in low frequency region our superconductor exhibit metamaterial property. This behavior is independent of the nonlinear parameter and can be seen for either linear (b=0) and nonlinear (b≠0) electrodynamics. Interestingly, for (3+1)-dimensional Lifshitz-dilaton holographic superconductors, we observe metamaterial behavior neither in the presence of linear nor nonlinear electrodynamics.

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].

Towards a gravity dual for the large scale structure of the universe

The dynamics of the large-scale structure of the universe enjoys at all scales, even in the highly non-linear regime, a Lifshitz symmetry during the matter-dominated period. In this paper we propose a general class of six-dimensional spacetimes which could be a gravity dual to the four-dimensional large-scale structure of the universe. In this set-up, the Lifshitz symmetry manifests itself as an isometry in the bulk and our universe is a four-dimensional brane moving in such six-dimensional bulk. After finding the correspondence between the bulk and the brane dynamical Lifshitz exponents, we find the intriguing result that the preferred value of the dynamical Lifshitz exponent of our observed universe, at both linear and non-linear scales, corresponds to a fixed point of the RGE flow of the dynamical Lifshitz exponent in the dual system where the symmetry is enhanced to the Schrodinger group containing a non-relativistic conformal symmetry. We also investigate the RGE flow between fixed points of the Lifshitz dynamical exponent in the bulk and observe that this flow is reflected in a growth rate of the large-scale structure, which seems to be in qualitative agreement with what is observed in current data. Our set-up might provide an interesting new arena for testing the ideas of holography and gravitational duals.

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 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.

Holographic quenches towards a Lifshitz point

We use the holographic duality to study quantum quenches of a strongly coupled CFT that drive the theory towards a non-relativistic fixed point with Lifshitz scaling. We consider the case of a Lifshitz dynamical exponent $z$ close to unity, where the non-relativistic field theory can be understood as a specific deformation of the corresponding CFT and, hence, the standard holographic dictionary can be applied. On the gravity side this amounts to finding a dynamical bulk solution which interpolates between AdS and Lishitz spacetimes as time evolves. We show that an asymptotically Lifshitz black hole is always formed in the final state. This indicates that it is impossible to reach the vacuum state of the Lifshitz theory from the CFT vacuum as a result of the proposed quenching mechanism. The nonequilibrium dynamics following the breaking of the relativistic scaling symmetry is also probed using both local and non-local observables. In particular, we conclude that the equilibration process happens in a top-down manner, i.e., the symmetry is broken faster for UV modes.

Effects of high-order operators in nonrelativistic Lifshitz holography

In this paper, we study the effects of high-order operators on the non-relativistic Lifshitz holography in the framework of the Ho\v{r}ava-Lifshitz (HL) theory of gravity, which naturally contains high-order operators in order for the theory to be power-counting renormalizble, and provides an ideal place for such studies. In particular, we show that the Lifshitz space-time is still a solution of the full theory of the HL gravity. The effects of the high-oder operators on the space-time itself is simply to shift the Lifshitz dynamical exponent. However, while in the infrared the asymptotic behavior of a (probe) scalar field near the boundary is similar to that studied in the literature, it gets dramatically modified in the UV limit, because of the presence of the high-order operators in this regime. Then, according to the gauge/gravity duality, this in turn affects the two-point correlation functions.

Lifshitz effects on vector condensate induced by a magnetic field

By numerical and analytical methods, we study in detail the effects of the Lifshitz dynamical exponent $z$ on the vector condensate induced by an applied magnetic field in the probe limit. Concretely, in the presence of the magnetic field, we obtain the Landau level independent of $z$, and we also find the critical value by coupling a Maxwell complex vector field and an SU(2) field into a ($3+1$)-dimensional Lifshitz black hole, respectively. The research results show that for the two models with the lowest Landau level, the increasing $z$ improves the response of the critical temperature to the applied magnetic field even without the charge density, and the analytical results uphold the numerical results. In addition, we find that, even in the Lifshitz black hole, the Maxwell complex vector model is still a generalization of the SU(2) Yang-Mills model. Furthermore, we construct the square vortex lattice and discuss the implications of these results.