CFT description of the Fully Frustrated XY model and phase diagram analysis

TL;DR

This paper uses conformal field theory to analyze the fully frustrated XY model, revealing its phase diagram and critical behavior through a flow between different CFTs.

Contribution

It introduces a CFT framework based on m-reduction to describe the FFXY model's symmetry and phase transitions, connecting it to known critical theories.

Findings

The c=2 twisted CFT accurately models the FFXY system.

The phase diagram is derived from flow between CFT vacua.

Critical behavior at the overlap temperature matches known transitions.

Abstract

Following a suggestion given in Nucl. Phys. B 300 (1988)611,we show how the U(1)*Z_{2} symmetry of the fully frustrated XY (FFXY) model on a square lattice can be accounted for in the framework of the m-reduction procedure developed for a Quantum Hall system at "paired states" fillings nu =1 (cfr. Cristofano et al.,Mod. Phys. Lett. A 15 (2000)1679;Nucl. Phys. B 641 (2002)547). The resulting twisted conformal field theory (CFT) with central charge c=2 is shown to well describe the physical properties of the FFXY model. In particular the whole phase diagram is recovered by analyzing the flow from the Z_{2} degenerate vacuum of the c=2 CFT to the infrared fixed point unique vacuum of the c=3/2 CFT. The last theory is known to successfully describe the critical behavior of the system at the overlap temperature for the Ising and vortex-unbinding transitions.