Spin-liquids on the triangular lattice in a spin model approximating the Hubbard model

The weak ordering tendency of the triangular-lattice antiferromagnetic nearest-neighbor Heisenberg model has drawn considerable attention to whether additional couplings or degrees of freedom might destabilize the order yielding a quantum spin liquid. Recently, the authors of [Phys. Rev. X 10, 021042 (2020)] provided numerical evidence that the tirangular-lattice Hubbard model in the vicinity of the Mott transition hosts a chiral spin-liquid (CSL) state spontaneously breaking time-reversal symmetry. However, past literature studying an effective SU(2) invariant spin Hamiltonian derived from a strong-coupling expansion reports not a CSL, but other states such as a U(1) spin liquid with spinon Fermi surface. To better understand the competition between these phases in the spin model, we use both exact diagonalization and the infinite density-matrix renormalization group to characterize the extended phase diagram of the spin Hamiltonian. We find that the CSL is the ground state in a finite parameter region as evidenced by spontaneous time-reversal symmetry breaking, a fractionally quantized spin Hall conductivity, and the expected chiral structure of the entanglement spectrum. We comment on the connection to the CSL in the Hubbard model and earlier reported spin liquid states.