Holographic End-Point of Spatially Modulated Phase Transition

TL;DR

This paper constructs and analyzes the end-point solutions of a spatially modulated phase transition in a holographic model, revealing a second-order transition at large coupling and a potential change to first order due to quantum effects, with notable conductivity properties.

Contribution

It provides the first non-linear solutions describing the end-point of the spatially modulated phase transition in a holographic setup, and explores how quantum corrections affect the transition order.

Findings

Second order phase transition with mean field critical exponent at large Chern-Simons coupling.

Quantum corrections may change the transition from second to first order.

Infinite off-diagonal DC conductivity in the new phase.

Abstract

In the previous paper [arXiv:0911.0679], we showed that the Reissner-Nordstrom black hole in the 5-dimensional anti-de Sitter space coupled to the Maxwell theory with the Chern-Simons term is unstable when the Chern-Simons coupling is sufficiently large. In the dual conformal field theory, the instability suggests a spatially modulated phase transition. In this paper, we construct and analyze non-linear solutions which describe the end-point of this phase transition. In the limit where the Chern-Simons coupling is large, we find that the phase transition is of the second order with the mean field critical exponent. However, the dispersion relation with the Van Hove singularity enhances quantum corrections in the bulk, and we argue that this changes the order of the phase transition from the second to the first. We compute linear response functions in the non-linear solution and find an infinite off-diagonal DC conductivity in the new phase.