Competing $U(1)$ and $\mathbb{Z}_2$ dipolar-octupolar quantum spin liquids on the pyrochlore lattice: application to Ce$_2$Zr$_2$O$_7$

TL;DR

This paper explores various quantum spin liquid states in Ce$_2$Zr$_2$O$_7$, using theoretical models to identify competing phases that match experimental observations, beyond the previously considered $U(1)$ quantum spin ice.

Contribution

It classifies all symmetric $U(1)$ and $bZ_2$ quantum spin liquids in the dipolar-octupolar model and constructs a phase diagram revealing competing gapped $bZ_2$ states relevant to experiments.

Findings

Identifies two closely competing gapped $bZ_2$ QSLs with narrow spinon dispersion.

Shows these QSLs have spin structure factors similar to neutron scattering data.

Highlights the importance of considering multiple QSL phases in interpreting experiments.

Abstract

Recent experiments on the dipolar-octupolar pyrochlore compound Ce$_2$Zr$_2$O$_7$ indicate that it may realize a three-dimensional quantum spin liquid (QSL). In particular, the analyses of available data suggest that the system is in a region of parameter space, where the so-called $\pi$-flux $U(1)$ octupolar quantum spin ice (QSI) with an emergent photon could be realized. On the other hand, because the system is far from the perturbative classical spin ice regime, it is unclear whether the quantum ground state is primarily a coherent superposition of 2-in-2-out configurations as in the canonical QSI phases. In this work, we explore other possible competing quantum spin liquid states beyond QSI using the Schwinger boson parton construction of the dipolar-octupolar pseudospin-1/2 model. After classifying all symmetric $U(1)$ and $\mathbb{Z}_2$ QSLs using the projective symmetry group (PSG), we construct a mean-field phase diagram that possesses a number of important features observed in an earlier exact diagonalization study. In the experimentally relevant frustrated region of the phase diagram, we find two closely competing gapped $\mathbb{Z}_2$ QSLs with a narrow spinon dispersion. The equal-time and dynamical spin structure factors of these states show key features similar to what was reported in neutron scattering experiments. Hence, these QSLs are closely competing ground states in addition to the $\pi$-flux $U(1)$ QSI, and they should be taken into account on equal footing for the interpretation of experiments on Ce$_2$Zr$_2$O$_7$.