Theory of quantum kagome ice and vison zero modes

Abstract

We derive an effective $Z_2$ gauge theory to describe the quantum kagome ice (QKI) state that has been observed by Carrasquilla $\text{et. al.}$ in Monte Carlo studies of the $S=1/2$ kagome XYZ model in a Zeeman field. The numerical results on QKI are consistent with, but do not confirm or rule out, the hypothesis that it is a $Z_2$ spin liquid. Our effective theory allows us to explore this hypothesis and make a striking prediction for future numerical studies, namely that symmetry-protected vison zero modes arise at lattice disclination defects, leading to a Curie defect term in the spin susceptibility, and a characteristic $(N_{dis}-1)\ln 2$ contribution to the entropy, where $N_{dis}$ is the number of disclinations. Only the $Z_2$ Ising symmetry is required to protect the vison zero modes. This is remarkable because a unitary $Z_2$ symmetry cannot be responsible for symmetry-protected degeneracies of local degrees of freedom. We also discuss other signatures of symmetry fractionalization in the $Z_2$ spin liquid, and phase transitions out of the $Z_2$ spin liquid to nearby ordered phases.

12 pages, 4 figures; v2 references updated

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Cited by in corpus (2)

• Fragmentation in Frustrated Magnets -- A review
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore