Semi-classical Approach to Quantum Spin Ice

TL;DR

This paper develops a semi-classical perturbative approach to analyze the low-energy excitations of quantum spin ice, revealing how photon interactions influence their properties and matching numerical results.

Contribution

It introduces a semi-classical Villain expansion method to analytically study quantum spin ice, capturing photon interactions and their effects on photon velocity and energy.

Findings

Photon-photon interactions renormalize photon speed

Splitting of transverse photon polarizations at intermediate wavevectors

Analytic photon velocity and ground state energy calculations

Abstract

We propose a semi-classical description of the low-energy properties of quantum spin ice in the strong Ising limit. Within the framework of a semiclassical, perturbative Villain expansion, that can be truncated at arbitrary order, we give an analytic and quantitative treatment of the deconfining phase. We find that photon-photon interactions significantly renormalise the speed of light and split the two transverse photon polarisations at intermediate wavevectors. We calculate the photon velocity and the ground state energy to first and second order in perturbation theory, respectively. The former is in good agreement with recent numerical simulations.