Charge Expulsion from Black Brane Horizons, and Holographic Quantum Criticality in the Plane

TL;DR

This paper uses holographic methods to study quantum criticality in 2+1 dimensions, revealing a charge expulsion phase transition in a 5+1-dimensional gravity model with Chern-Simons interactions, leading to different IR geometries and entropy behaviors.

Contribution

It introduces a holographic model with Chern-Simons coupling to describe charge expulsion and quantum criticality, identifying a phase transition at a critical coupling k_c.

Findings

Charge is expelled from the black brane horizon at k=k_c.

Near-horizon geometry transitions from Lifshitz to AdS_4 imes R^2.

Entropy density vanishes quadratically at the IR fixed point.

Abstract

Quantum critical behavior in 2+1 dimensions is established via holographic methods in a 5+1-dimensional Einstein gravity theory with gauge potential form fields of rank 1 and 2. These fields are coupled to one another via a tri-linear Chern-Simons term with strength k. The quantum phase transition is physically driven by the expulsion of the electric charge from inside the black brane horizon to the outside, where it gets carried by the gauge fields which acquire charge thanks to the Chern-Simons interaction. At a critical value k=k_c, zero temperature, and any finite value of the magnetic field, the IR behavior is governed by a near-horizon Lifshitz geometry. The associated dynamical scaling exponent depends on the magnetic field. For k<k_c, the flow towards low temperature is governed by a Reissner-Nordstrom-like black brane whose charge and entropy density are non-vanishing at zero temperature. For k > k_c, the IR flow is towards the purely magnetic brane in AdS_6. Its near-horizon geometry is AdS_4 \times R^2, so that the entropy density vanishes quadratically with temperature, and all charge is carried by the gauge fields outside of the horizon.