Holographic model of superfluidity

TL;DR

The paper investigates a relativistic superfluid with a global U(1) symmetry using a holographic dual, modeling a charged scalar in AdS coupled to a gauge field in the probe limit. It analyzes thermodynamics, hydrodynamics, and the phase structure under nonzero superfluid current, revealing a second-order transition at low current and a current-driven first-order transition with a tricritical point, along with the behavior of second sound. Phase diagrams for two boundary operator dimensions demonstrate how μ and ξ control the transition and condensate, linking holographic dynamics to Landau-Ginzburg intuition. The work provides a framework to compute transport properties and dynamic responses from the gravity dual, with clear paths to include backreaction and to study density-density correlators for a fuller hydrodynamic picture.

Abstract

We study a holographic model of a relativistic quantum system with a global U(1) symmetry, at non-zero temperature and density. When the temperature falls below a critical value, we find a second-order superfluid phase transition with mean-field critical exponents. In the symmetry-broken phase, we determine the speed of second sound as a function of temperature. As the velocity of the superfluid component relative to the normal component increases, the superfluid transition goes through a tricritical point and becomes first-order.

Figures (4)

• Figure 1: The phase diagrams for the theory with a scalar with a) conformal dimension one and b) conformal dimension two. The solid blue line indicates a second order phase transition while the solid red line (in between the dashed lines) indicates a first order phase transition. The dashed blue lines are spinodal curves, while the red dot indicates the tricritical point.
• Figure 2: The condensate as a function of temperature for the two operators: (a) $O_1$ and (b) $O_2$. The curves in the plots, from right to left, are for $\xi / \mu = 0$, $1/4$, $1/3$, $2/5$, and $1/2$.
• Figure 3: The difference in free energy $\Delta \Omega_1$ between the phase with a scalar condensate and without one as a function of $T/\mu$: a) $\xi=0$ and b) $\xi/\mu = 4/7$.
• Figure 4: The speed of second sound as a function of $T/\mu$, computed by evaluating thermodynamic derivatives in Eq. (\ref{['eq:second-sound-leftover']}): a) $O_1$ scalar, b) $O_2$ scalar. The speed of second sound vanishes as $T\to T_c$ and appears to approach a constant value as $T\to 0$.