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The family of Kitaev materials provides an ideal platform to study quantum spin liquids and their neighboring magnetic orders. Motivated by the possibility of a quantum spin liquid ground state in pressurized hyperhoneycomb iridate $beta$-Li$_2$IrO$_3$, we systematically classify and study symmetric quantum spin liquids on the hyperhoneycomb lattice, using the Abrikosov-fermion representation. Among the 176 symmetric $U(1)$ spin liquids (and 160 $Z_2$ spin liquids), we identify 8 root $U(1)$ spin liquids in proximity to the ground state of the solvable Kitave model on hyperhonecyomb lattices. These 8 states are promising candidates for possible $U(1)$ spin liquid ground states in pressurized $beta$-Li$_2$IrO$_3$. We further discuss physical properties of these 8 $U(1)$ spin liquid candidates, and show that they all support nodal-line-shaped spinon Fermi surfaces.
We study the effective spin-orbital model that describes the magnetism of 4$d^1$ or 5$d^1$ Mott insulators in ideal tricoordinated lattices. In the limit of vanishing Hunds coupling, the model has an emergent SU(4) symmetry which is made explicit by
Quantum spin liquids are an exciting playground for exotic physical phenomena and emergent many-body quantum states. The realization and discovery of quantum spin liquid candidate materials and associated phenomena lie at the intersection of solid-st
We review recent density-matrix renormalization group (DMRG) studies of lightly doped quantum spin liquids (QSLs) on the kagome lattice. While a number of distinct conducting phases, including high-temperature superconductivity, have been theoretical
We construct and study quantum trimer models and resonating SU(3)-singlet models on the kagome lattice, which generalize quantum dimer models and the Resonating Valence Bond wavefunctions to a trimer and SU(3) setting. We demonstrate that these model
We study the nearest neighbor $XXZ$ Heisenberg quantum antiferromagnet on the kagome lattice. Here we consider the effects of several perturbations: a) a chirality term, b) a Dzyaloshinski-Moriya term, and c) a ring-exchange type term on the bowties