Lifshitz effects on holographic p-wave superfluid

Ya-Bo Wu,Jun-Wang Lu,Cheng-Yuan Zhang,Nan Zhang,Xue Zhang,Zhuo-Qun Yang,Si-Yu Wu

doi:10.1016/j.physletb.2014.12.026

Abstract

In the probe limit, we numerically build a holographic p-wave superfluid model in the four-dimensional Lifshitz black hole coupled to a Maxwell-complex vector field. We observe the rich phase structure and find that the Lifshitz dynamical exponent z contributes evidently to the effective mass of the matter field and dimension of the gravitational background. Concretely, we obtain that the Cave of Winds appeared only in the five-dimensional anti-de Sitter (AdS) spacetime, and the increasing z hinders not only the condensate but also the appearance of the first-order phase transition. Furthermore, our results agree with the Ginzburg–Landau results near the critical temperature. In addition, the previous AdS superfluid model is generalized to the Lifshitz spacetime.

Highlights

The gauge/gravity duality [1] builds a powerful relationship between the many-body system in the quantum mechanics with the strong interaction and the classical dynamical black hole with a higher dimension of spacetime, in the past decades, it has been widely used to study various strongly coupled system
To see the anisotropic effects, some holographic superconductors were constructed in the Lifshitz black hole backgrounds, see, for example, Refs. [23,24,25,26,27,28,29,30,31,32,33], where the results showed that the larger Lifshitz parameter z hinders the condensate
More interesting questions are whether we can see (i) the Cave of Winds only existed in the 5D anti-de Sitter (AdS) black hole when considering the effects of Lifshitz parameter z on the dimension of the gravitational background; (ii) the disappearance of the first-order phase transition due to the fact that the larger parameter z hinders the condensate

Summary

INTRODUCTION

The gauge/gravity duality [1] builds a powerful relationship between the many-body system in the quantum mechanics with the strong interaction and the classical dynamical black hole with a higher dimension of spacetime, in the past decades, it has been widely used to study various strongly coupled system. More interesting questions are whether we can see (i) the Cave of Winds only existed in the 5D AdS black hole when considering the effects of Lifshitz parameter z on the dimension of the gravitational background; (ii) the disappearance of the first-order phase transition due to the fact that the larger parameter z hinders the condensate. Answering these questions is just the purpose of this paper. The last section is devoted to the conclusions and further discussions

EQUATIONS OF MOTION AND THE GRAND POTENTIAL

CONDENSATES VERSUS THE TEMPERATURE

4: The condensate versus the temperature for

SUPERCURRENTS VERSUS THE SUPERFLUID VELOCITY

CONCLUSION AND DISCUSSION