Spin nematic ground state of the triangular lattice S=1 biquadratic model

Motivated by the spate of recent experimental and theoretical interest in Mott insulating S=1 triangular lattice magnets, we consider a model S=1 Hamiltonian on a triangular lattice interacting with rotationally symmetric biquadratic interactions. We show that the partition function of this model can be expressed in terms of configurations of three colors of tightly packed closed loops with non-negative weights, which allows for efficient quantum Monte Carlo sampling on large lattices. We find that the ground state has spin nematic order, i.e., it spontaneously breaks spin rotation symmetry but preserves time-reversal symmetry. We present accurate results for the parameters of the low-energy field theory as well as finite-temperature thermodynamic functions.