Holographic End-Point of Spatially Modulated Phase Transition

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.

Figures (11)

• Figure 1: Double well potential $U$ for a classical particle with coordinate $h$. If the particle starts slightly outside of the origin, say at $A$, then the particle will oscillate between $A$ and another point $B$ with the same potential energy.
• Figure 2: The amplitude $h$ and the energy density $\mathcal{H}$ as a function of $k$.
• Figure 3: Critical temperature as a function of the Chern-Simons coupling $\alpha$. The shaded region indicates a phase with a non-zero expectation value of the conserved current $\vec{J}$ which is helical and position dependent.
• Figure 4: The amplitude $h_0$ and the energy density difference $\Delta \widetilde{\mathcal{H}}$ from the homogeneous phase as functions of $k$.
• Figure 5: The expectation value of the order parameter as a function of the temperature. The dotted curve is the numerical result and the solid curve is its fit with $(1-\tau/\tau_c)^{1/2}$.