Classification and correlation signatures of chiral spin liquids on the pyrochlore lattice

TL;DR

This paper systematically classifies chiral quantum spin liquids on the pyrochlore lattice, analyzing their symmetry, flux, and spinon spectra, and introduces diagnostics to distinguish different gauge regimes.

Contribution

It provides a detailed classification and variational analysis of chiral spin liquids, including diagnostics for gauge dominance and flux sector distinctions.

Findings

Different flux sectors show distinct gauge-field dominance.

Correlation diagnostics can distinguish Coulomb and matter-field contributions.

Chiral spin liquids are proximate phases relevant to extended pyrochlore models.

Abstract

We present a systematic classification and variational study of chiral quantum spin liquids on the pyrochlore lattice based on fermionic parton constructions. Focusing on chiral $\mathrm{U(1)}$ and $\mathbb{Z}_2$ spin-liquid Ans\"atze, we characterize their symmetry properties, flux structures, and low-energy spinon spectra within a projective symmetry group framework, and incorporate gauge fluctuations through Gutzwiller-projected wave functions studied by variational Monte Carlo. From the equal-time spin structure factor, we develop correlation-based diagnostics that distinguish gauge-dominated Coulomb phases from states with substantial matter-field and short-range contributions. Distinct chiral flux sectors, though close in energy, exhibit markedly different degrees of emergent $\mathrm{U(1)}$ gauge-field dominance, reflected in the geometry and contrast of pinch-point singularities. Although these states are not competitive ground states of the nearest-neighbor Heisenberg model, they define a physically meaningful family of proximate chiral phases relevant to extended pyrochlore Hamiltonians.