Symmetry fractionalization in the gauge mean-field theory of quantum spin ice

TL;DR

This paper extends gauge mean-field theory to classify symmetry fractionalization in quantum spin ice, revealing new states and predicting experimental signatures for different symmetry-enriched phases.

Contribution

It introduces a framework for classifying space-time symmetry fractionalization in GMFT of quantum spin ice, including new chiral U(1) quantum spin liquid states.

Findings

Only two U(1) gauge states respect all space-group symmetries.

Discovered two new chiral U(1) QSI states with fluxes of π/2 and 3π/2.

Predicted distinct neutron scattering signatures for different fractionalization patterns.

Abstract

Symmetry fractionalization is a ubiquitous feature of topologically ordered states that can be used to classify different symmetry-enriched topological phases and reveal some of their unique experimental signatures. Despite its vast popularity, there is currently no available framework to study symmetry fractionalization of quantum spin ice (QSI) -- a $U(1)$ quantum spin liquid (QSL) on the pyrochlore lattice supporting emergent photons -- within the most widely used theoretical framework to describe it, gauge mean-field theory (GMFT). In this work, we provide an extension of GMFT that allows for the classification of space-time symmetry fractionalization. The construction classifies all GMFT Ans\"atze that yield physical wavefunctions invariant under given symmetries and a specific low-energy gauge structure. As an application of the framework, we first show that the only two Ans\"atze with emergent $U(1)$ gauge fields that respect all space-group symmetries are the well-known 0- and $\pi$-flux states. We then showcase how the framework may describe QSLs beyond the currently known ones by classifying chiral $U(1)$ QSI. We find two new states described by $\pi/2$- and $3\pi/2$-fluxes of the emergent gauge field threading the hexagonal plaquettes of the pyrochlore lattice. We finally discuss how the different ways translation symmetries fractionalize for all these states lead to unique experimentally relevant signatures and compute their respective inelastic neutron scattering cross-section to illustrate the argument.