Quantum phase transitions in holographic models of magnetism and superconductors

Abstract

We study a holographic model realizing an ``antiferromagnetic'' phase in which a global $SU(2)$ symmetry representing spin is broken down to a $U(1)$ by the presence of a finite electric charge density. This involves the condensation of a neutral scalar field in a charged anti--de Sitter black hole. We observe that the phase transition for both neutral and charged (as in the standard holographic superconductor) order parameters can be driven to zero temperature by a tuning of the UV conformal dimension of the order parameter, resulting in a quantum phase transition of the Berezinskii-Kosterlitz-Thouless--type. We also characterize the antiferromagnetic phase and an externally forced ferromagnetic phase by showing that they contain the expected spin waves with linear and quadratic dispersions, respectively.