Topological aspects of symmetry breaking in triangular-lattice Ising antiferromagnets

TL;DR

This paper explores the topological phenomena and phase transitions in a triangular-lattice Ising antiferromagnet with extended interactions, revealing an intermediate nematic phase and fractional excitations.

Contribution

It introduces a novel Monte Carlo algorithm and uncovers a split first-order transition with a topologically rich intermediate phase in the model.

Findings

Identification of an intermediate nematic phase with algebraic correlations

Discovery of fractional edge excitations in the stripe state

Observation of a Kasteleyn transition between domain wall configurations

Abstract

Using a specially designed Monte Carlo algorithm with directed loops, we investigate the triangular lattice Ising antiferromagnet with coupling beyond nearest neighbour. We show that the first-order transition from the stripe state to the paramagnet can be split, giving rise to an intermediate nematic phase in which algebraic correlations coexist with a broken symmetry. Furthermore, we demonstrate the emergence of several properties of a more topological nature such as fractional edge excitations in the stripe state, the proliferation of double domain walls in the nematic phase, and the Kasteleyn transition between them. Experimental implications are briefly discussed.