We study the quantum phase transition between the
Z2 spin liquid and valence bond solid (VBS) orders on a triangular lattice. With a fully isotropic triangular lattice, the transition from a columnar or resonating-plaquette VBS order can either be first order or there could be two transitions with an intermediate phase. If the transition splits into two, then the
Z2 spin liquid will first experience a first-order
q=3 Potts transition to a new nematic
Z2 spin liquid that breaks the $2\ensuremath{\pi}/3$ lattice rotation symmetry (but retain translation symmetry, unlike the VBS states). The second transition will then take this new nematic
Z2 spin liquid to a columnar or resonating-plaquette VBS state through a second-orderthree-dimensional (3D)
XY∗ transition. On a distorted triangular lattice, the degeneracy between some of the different columnar VBS orders is lifted, and the phase transition can reduce to a single 3D
XY∗ transition.
Resonating valence bond (RVB) states are fundamental for understanding quantum spin liquids in two-dimensional (2D) systems. The RVB state is a collective phenomenon in which spins are uncoupled. 2D lattices such as triangular, honeycomb, and dice lattices were investigated using the Hubbard model and exact diagonalization method. We analyzed the total spin, spin-spin correlation functions, local magnetic moments, and spin and charge gaps as a function of on-site Coulomb repulsion, electron concentration, and electronic hopping parameters. Phase diagrams showed that RVB states can live in half-filled and hole-doped anisotropic triangular lattices. We found two types of RVB states: one in the honeycomb sublattice and the other in the centered hexagons in the triangular lattices. Owing to the novel discovery of exotic magnetic ordering in triangular moiré patterns in twisted bilayer graphene and transition metal dichalcogenide systems, our results provide physical insights into the onset of magnetism and possible spin liquid states in these layered materials.
We introduce a Monte Carlo scheme based on sampling of Pfaffians to investigate Anderson's resonating-valence-bond (RVB) spin liquid wave function on the kagome and the triangular lattice. This eliminates a sign problem that prevents utilization of the valence bond basis in Monte Carlo studies for nonbipartite lattices. Studying lattice sizes of up to 600 sites, we calculate singlet-singlet and spin-spin correlations and demonstrate how the lattice symmetry is restored within each topological sector as the system size is increased. Our findings are consistent with the expectation that the nearest-neighbor RVB states describe a topological spin liquid on these nonbipartite lattices.