Non Mean-Field Quantum Critical Points from Holography

TL;DR

This paper constructs a class of quantum critical points with non-mean-field exponents using holography, interpolating between different types of phase transitions and highlighting the role of an emergent infrared theory.

Contribution

It introduces a phenomenological holographic model that demonstrates non-mean-field quantum critical points and explores their properties and dependence on parameters.

Findings

Identifies a line of quantum critical points with non-mean-field exponents.

Shows the transition interpolates between mean-field and BKT types.

Demonstrates non-mean-field scaling is destroyed at nonzero temperature.

Abstract

We construct a class of quantum critical points with non-mean-field critical exponents via holography. Our approach is phenomenological. Beginning with the D3/D5 system at nonzero density and magnetic field which has a chiral phase transition, we simulate the addition of a third control parameter. We then identify a line of quantum critical points in the phase diagram of this theory, provided that the simulated control parameter has dimension less than two. This line smoothly interpolates between a second-order transition with mean-field exponents at zero magnetic field to a holographic Berezinskii-Kosterlitz-Thouless transition at larger magnetic fields. The critical exponents of these transitions only depend upon the parameters of an emergent infrared theory. Moreover, the non-mean-field scaling is destroyed at any nonzero temperature. We discuss how generic these transitions are.