Quantum Spin Liquid in a Distorted Kagome Lattice and the Pyrochlore Lattice

The Kagome-lattice-based material, volborthite, has been considered as a promising platform for the discovery of exotic quantum ground states. Using projective symmetry group (PSG) analysis and Schwinger boson mean field theory, we explore the possible quantum spin liquid (QSL) and magnetically ordered phases in a two-dimensional nonsymmorphic lattice described by the plane crystallographic group p2gg [1], which is consistent with the spatial anisotropy of the spin model of volborthite derived from density functional theory. We find that the QSL ground state is related to a coplanar incommensurate spiral order, while a closely competing QSL state is related to a spin density wave order. In addition, periodicity enhancement of the two spinon spectrum is observed in the competing QSL state as a result of symmetry fractionalization. Finally, we discuss the correspondence between the bosonic and fermionic QSL states through vison PSG [2].
On the other hand, as an ongoing project, we also study the possible realization of QSL in the three-dimensional pyrochlore lattice.

References
1. Chern et al, Phys. Rev. B 96, 035118 (2017)
2. Chern et al, Phys. Rev. B 96, 165117 (2017)