Magnetic Field Induced Quantum Criticality via new Asymptotically AdS_5 Solutions

TL;DR

This paper derives new analytical solutions in holography that reveal quantum critical behavior induced by magnetic fields, showing a critical point with specific thermodynamic scaling laws and a dynamical exponent z=3.

Contribution

The authors present the first analytical asymptotically AdS_5 solutions at zero temperature with zero entropy, capturing quantum criticality in holographic duals with magnetic fields.

Findings

Identification of a quantum critical point at a lower bound of magnetic field to charge density ratio.

Derivation of a scaling law s ~ T^{1/3} at the critical magnetic field.

Determination of the dynamical critical exponent z=3.

Abstract

Using analytical methods, we derive and extend previously obtained numerical results on the low temperature properties of holographic duals to four-dimensional gauge theories at finite density in a nonzero magnetic field. We find a new asymptotically AdS_5 solution representing the system at zero temperature. This solution has vanishing entropy density, and the charge density in the bulk is carried entirely by fluxes. The dimensionless magnetic field to charge density ratio for these solutions is bounded from below, with a quantum critical point appearing at the lower bound. Using matched asymptotic expansions, we extract the low temperature thermodynamics of the system. Above the critical magnetic field, the low temperature entropy density takes a simple form, linear in the temperature, and with a specific heat coefficient diverging at the critical point. At the critical magnetic field, we derive the scaling law s ~ T^{1/3} inferred previously from numerical analysis. We also compute the full scaling function describing the region near the critical point, and identify the dynamical critical exponent: z=3. These solutions are expected to holographically represent boundary theories in which strongly interacting fermions are filling up a Fermi sea. They are fully top-down constructions in which both the bulk and boundary theories have well known embeddings in string theory.