The Many Phases of Holographic Superfluids

TL;DR

This paper explores the phase structure of holographic superfluids in different dimensions, revealing universal behaviors in three dimensions and complex transitions in four dimensions, including analytical insights at high velocities.

Contribution

It provides a detailed analysis of phase transitions in holographic superfluids across different dimensions and introduces a double scaling limit for analytical study at high velocities.

Findings

In d=3, phase transition order changes with superfluid velocity.

In d=4, high mass leads to persistent second order transitions.

A double scaling limit allows analytical exploration of phase transitions.

Abstract

We investigate holographic superfluids in AdS_{d+1} with d=3,4 in the non-backreacted approximation for various masses of the scalar field. In d=3 the phase structure is universal for all the masses that we consider: the critical temperature decreases as the superfluid velocity increases, and as it is cranked high enough, the order of the phase transition changes from second to first. Surprisingly, in d=4 we find that the phase structure is more intricate. For sufficiently high mass, there is always a second order phase transition to the normal phase, no matter how high the superfluid velocity. For some parameters, as we lower the temperature, this transition happens before a first order transition to a new superconducting phase. Across this first order transition, the gap in the transverse conductivity jumps from almost zero to about half its maximum value. We also introduce a double scaling limit where we can study the phase transitions (semi-)analytically in the large velocity limit. The results corroborate and complement our numerical results. In d=4, this approach has the virtue of being fully analytically tractable.