Magnetic Field Induced Quantum Criticality via new Asymptotically AdS_5 Solutions

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.

Figures (2)

• Figure 1: Schematic phase diagram illustrating the various behaviors of the entropy density versus temperature and magnetic field. The region inside the dashed line is controlled by the quantum critical point at $(\hat{T}=0,\hat{B}=\hat{B}_c)$, and the entropy density can be expressed in terms of a single scaling function $f$ of $(\hat{B} - \hat{B}_c)/T^{2/3}$. We move around inside this region by changing the temperature $\hat{T}$ and the relevant coupling $\hat{B}-\hat{B}_c$. The boundary of the region is defined to be where irrelevant operators become important. The yellow region denotes a regime where temperature is the largest energy scale, corresponding to the argument of the scaling function $f$ being small. Outside the yellow region the low temperature behavior of the entropy density, for fixed $\hat{B}$, is either constant or linear in $\hat{T}$, depending on whether the quantum critical point is approached from below or from above $\hat{B}_c$ as $\hat{T}\rightarrow 0$.
• Figure 2: Numerical solution of (\ref{['LVeqtns']}) for $V(r)$ and $L(r)$ subject to boundary conditions (\ref{['VLas']})