Holographic Berezinskii-Kosterlitz-Thouless Transitions

TL;DR

The first example of a quantum Berenzinskii-Kosterlitz-Thouless (BKT) phase transition in two spatial dimensions via holography is found in the D3/D5 system at nonzero density and magnetic field.

Abstract

We find the first example of a quantum Berenzinskii-Kosterlitz-Thouless (BKT) phase transition in two spatial dimensions via holography. This transition occurs in the D3/D5 system at nonzero density and magnetic field. At any nonzero temperature, the BKT scaling is destroyed and the transition becomes second order with mean-field exponents. We go on to conjecture about the generality of quantum BKT transitions in two spatial dimensions.

Figures (1)

• Figure 1: A plot of the condensate as a function of magnetic field at zero and finite temperature near the zero-temperature transition. The dashed black line indicates zero-temperature numerical data and the solid blue line our prediction, Eq. (\ref{['sigmaPredict']}), computed further to ${\cal O}(\alpha^3)$. The color dashed curves represent numerical data at temperatures of $T=\frac{2}{\pi}\rho^{1/2}\times 10^{-11}$ (left) and $T=\frac{2}{\pi}\rho^{1/2}\times 10^{-10}$ (right). At any nonzero temperature, the condensate scales with a mean-field exponent near the transition and then asymptotes to the BKT scaling at large magnetic field.