A magnetically induced quantum phase transition in holography

TL;DR

This paper explores a quantum phase transition in a 2+1D gauge theory using holography, revealing a line of second order fixed points influenced by magnetic field and charge, with potential implications for understanding high-temperature superconductors.

Contribution

It introduces an analytical holographic model showing a line of second order fixed points in a 2+1D gauge theory at finite magnetic field and charge, connecting gravity solutions to quantum critical phenomena.

Findings

Discovery of a line of second order fixed points at B=B_c(χ).

Analytical extremal dyonic black-brane solutions with scalar profiles.

Similar behavior of the condensate to NJL models.

Abstract

We investigate quantum phase transitions in a 2+1 dimensional gauge theory at finite chemical potential $\chi$ and magnetic field $B$. The gravity dual is based on 4D $\mathcal{N}=2$ Fayet-Iliopoulos gauged supergravity and the solutions we consider---that are constructed analytically---are extremal, dyonic, asymptotically $AdS_4$ black-branes with a nontrivial radial profile for the scalar field. We discover a line of second order fixed points at $B=B_c(\chi)$ between the dyonic black brane and an extremal "thermal gas" solution with a singularity of good-type, according to the acceptability criteria of Gubser [1]. The dual field theory is the ABJM theory [2] deformed by a triple trace operator $\Phi^3$ and placed at finite charge and magnetic field. This line of fixed points might be useful in studying the various strongly interacting quantum critical phenomena such as the ones proposed to underlie the cuprate superconductors. We also find curious similarities between the behaviour of the VeV $\langle \Phi \rangle$ under B and that of the quark condensate in 2+1 dimensional NJL models.