${\mathbb{Z}}_2$ gauge theory for valence bond solids on the kagome lattice

Abstract

We present an effective ${\mathbb{Z}}_2$ gauge theory that captures various competing phases in spin-1/2 kagome lattice antiferromagnets: the topological ${\mathbb{Z}}_2$ spin liquid (SL) phase, and the 12-site and 36-site valence bond solid (VBS) phases. Our effective theory is a generalization of the recent ${\mathbb{Z}}_2$ gauge theory proposed for SL phases by Wan and Tchernyshyov. In particular, we investigate possible VBS phases that arise from vison condensations in the SL. In addition to the 12-site and 36-site VBS phases, there exists 6-site VBS that is closely related to the symmetry-breaking valence bond modulation patterns observed in the recent density matrix renormalization group simulations. We find that our results have remarkable consistency with a previous study using a differnt ${\mathbb{Z}}_2$ gauge theory. Motivated by the lattice geometry in the recently reported vanadium oxyfluoride kagome antiferromagnet, our gauge theory is extended to incorporate lowered symmetry by inequivalent up- and down-triangles. We investigate effects of this anisotropy on the 12-site, 36-site, and 6-site VBS phases. The 12-site VBS is stable to anisotropy while the 36-site VBS undergoes severe dimer melting. Interestingly, any analogue of the 6-site VBS is not found in this approach. We discuss the implications of these findings and also compare the results with a different type of ${\mathbb{Z}}_2$ gauge theory used in previous studies.

18 pages, 14 figures, 5 tables, updated with the published version

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• Evidence for a Parity Broken Monoclinic Ground State in the S = 1/2 Kagomé Antiferromagnet Herbertsmithite
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• Vison condensation and spinon confinement in a kagome-lattice ${\mathbb{Z}}_2$ spin liquid: A numerical study of a quantum dimer model
• Topical review: the nature of the ground state and possibility of a quantum spin liquid in 1T metal dichalcogenides
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