Dualities and the phase diagram of the $p$-clock model

TL;DR

This paper introduces a bond-algebraic duality approach to analyze the phase diagram and topological excitations of the two-dimensional XY and p-clock models, revealing emergent symmetries and critical phases.

Contribution

It develops a novel bond-algebraic method to study dualities, uncovering non-Abelian symmetries and the emergence of continuous U(1) symmetry for p ≥ 5 in the p-clock model.

Findings

Existence of non-Abelian symmetries in the models.

Emergence of continuous U(1) symmetry for p ≥ 5.

Identification of a critical intermediate phase with power-law correlations.

Abstract

A new "bond-algebraic" approach to duality transformations provides a very powerful technique to analyze elementary excitations in the classical two-dimensional XY and $p$-clock models. By combining duality and Peierls arguments, we establish the existence of non-Abelian symmetries, the phase structure, and transitions of these models, unveil the nature of their topological excitations, and explicitly show that a continuous U(1) symmetry emerges when $p \geq 5$. This latter symmetry is associated with the appearance of discrete vortices and Berezinskii-Kosterlitz-Thouless-type transitions. We derive a correlation inequality to prove that the intermediate phase, appearing for $p\geq 5$, is critical (massless) with decaying power-law correlations.