# Pyrochlore U(1) spin liquid of mixed symmetry enrichments in magnetic fields

## TL;DR

This paper explores the experimental detection and theoretical understanding of symmetry-enriched U(1) quantum spin liquids in pyrochlore materials, emphasizing the octupolar $ ext{pi}$-flux state and its magnetic field responses.

## Contribution

It introduces the concept of a $ ext{pi}$-flux U(1) QSL in pyrochlore magnets, highlighting its unique symmetry enrichment and experimental signatures, especially in Ce-based compounds.

## Key findings

- Prediction of magnetic field responses for octupolar $ ext{pi}$-flux U(1) QSLs
- Identification of symmetry enrichment from point group and translational symmetries
- Discussion of experimental relevance for Ce$_2$Sn$_2$O$_7$ and Ce$_2$Zr$_2$O$_7$

## Abstract

We point out the experimental relevance and the detection scheme of symmetry enriched U(1) quantum spin liquids (QSLs) outside the perturbative spin-ice regime. Recent experiments on Ce-based pyrochlore QSL materials suggest that the candidate QSL may not be proximate to the well-known spin ice regime, and thus differs fundamentally from other pyrochlore QSL materials. We consider the possibility of the $\pi$-flux U(1) QSL favored by frustrated transverse exchange interactions rather than the usual quantum spin ice. It was previously suggested that both dipolar U(1) QSL and octupolar U(1) QSL can be realized for the generic spin model for the dipole-octupole doublets of the Ce$^{3+}$ local moments on the pyrochlore magnets Ce$_2$Sn$_2$O$_7$ and Ce$_2$Zr$_2$O$_7$. We explain and predict the experimental signatures especially the magnetic field response of the octupolar $\pi$-flux U(1) QSL. Fundamentally, this remarkable state is a mixture of symmetry enrichments from point group symmetry and from translational symmetry. We discuss the relevant experiments for pyrochlore U(1) QSLs and further provide some insights to the pyrochlore Heisenberg model.