Emergent Power-Law Phase in the 2D Heisenberg Windmill Antiferromagnet: A Computational Experiment

TL;DR

This study uses computational experiments to demonstrate that an isotropic 2D Heisenberg antiferromagnet can develop algebraic spin correlations and exhibit a critical phase with emergent U(1) order, including BKT transitions and long-range order.

Contribution

It provides computational evidence for Polyakov's conjecture by showing emergent algebraic correlations and phase transitions in a 2D Heisenberg antiferromagnet with complex lattice structure.

Findings

Emergence of algebraic spin correlations at intermediate temperatures.

Identification of Berezinskii-Kosterlitz-Thouless phase transitions.

Observation of long-range Z6 order at low temperatures.

Abstract

In an extensive computational experiment, we test Polyakov's conjecture that under certain circumstances an isotropic Heisenberg model can develop algebraic spin correlations. We demonstrate the emergence of a multi-spin $\text{U(1)}$ order parameter in a Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. The correlations of this relative phase angle are observed to decay algebraically at intermediate temperatures in an extended critical phase. Using finite-size scaling, we show that both phase transitions are of the Berezinskii-Kosterlitz-Thouless type and at lower temperatures, we find long-range $\mathbb{Z}_6$ order.