Abstract
We explore the phase structure of a holographic toy model of superfluid states in non-relativistic conformal field theories. At low background mass density, we found a familiar second-order transition to a superfluid phase at finite temperature. Increasing the chemical potential for the probe charge density drives this transition strongly first order as the low-temperature superfluid phase merges with a thermodynamically disfavored high-temperature condensed phase. At high background mass density, the system re-enters the normal phase as the temperature is lowered further, hinting at a zero-temperature quantum phase transition as the background density is varied. Given the unusual thermodynamics of the background black hole, however, it seems likely that the true ground state is another configuration altogether.
Highlights
Non-relativistic superfluids provide a high-precision laboratory in which to probe many-body physics in the extreme quantum regime [1]
Similar effects arise in the holographic renormalization of the theory, which as usual requires introducing counterterms which depend on the boundary operator dimensions; here, these counterterms will explicitly depend on the boundary values of some bulk fields, too
The geometry is controlled by two physical parameters, the background mass density, Ω, and the temperature, T,with the horizon located at the radial coordinate rH =−1/3
Summary
Non-relativistic superfluids provide a high-precision laboratory in which to probe many-body physics in the extreme quantum regime [1]. In an effort to bring the tools of holography [2, 3, 4] to bear on these systems, considerable effort has been devoted to studying non-relativistic deformations of relativistic examples which enjoy z = 2 scaling [7, 8, 9, 10, 11] Such deformations generate highly atypical states in the resulting NRCFT whose thermodynamic and other properties are tightly constrained by their relativistic births. Taking the operator to be marginal in the NRCFT [5, 6] requires it to be irrelevant in the CFT This corresponds to a 1-parameter deformation of the geometry which alters the asymptotic geometry from Anti de Sitter (AdS), whose isometries form the relativistic conformal group, to Schrodinger [7, 8], whose isometries fill out the non-relativistic conformal group.
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