Gauge-Free Duality in Pure Square Spin Ice: Topological Currents and Monopoles

TL;DR

This paper introduces a gauge-free duality framework for pure square spin ice, describing topological currents and monopoles through a continuous field theory, enabling analysis of correlations and susceptibilities.

Contribution

It presents a novel gauge-free duality approach that models spin ice using topological charges and currents, extending the height formalism to finite temperatures and experimental systems.

Findings

Derived structure factors, correlations, and susceptibilities for spins, monopoles, and currents.

Established a continuous field theory framework for pure square spin ice.

Connected the theory to recent experimental realizations on quantum annealers.

Abstract

We consider a pure square spin ice, that is a square ice where only nearest neighbors are coupled. A gauge-free duality between the perpendicular and collinear structure leads to a natural description in terms of topological currents and charges as the relevant degrees of freedom. That, in turn, can be expressed via a continuous field theory where the discrete spins are subsumed into entropic interactions among charges and currents. This approach produces structure factors, correlations, and susceptibilities for spins, monopoles, and currents. It also generalizes to non-zero temperature the height formalism of the disordered ground state. The framework can be applied to a zoology of recent experimental results, especially realizations on quantum annealers and can be expanded to include longer range interactions.