DMRG Study of a Time-Reversal Symmetry Breaking Phase without Magnetism

Invariably, states of matter that break time-reversal symmetry (TRS) are associated with some form of magnetism. Recently, a phase was conjectured as an exception - it breaks TRS via chiral ordering of spins along a particular direction, but is spin-rotation symmetric (Ref: Hosur, arXiv:1510.00975). In this work, we prove the existence of such a state by performing a density matrix renormalization group (DMRG) study of a spin-1 chain with biquadratic interactions at zero temperature, and show that the ground state breaks TRS via anti-ferromagnetic chiral ordering of the spins, but is spin-rotation symmetric.