Study of phase transitions near SU(3) points in spin-1 systems using the Tensor Renormalisation Group

Quantum spin-1 systems allow for non-geometric frustration between bilinear and biquadratic interactions. For these systems frustration leads to a rich phase diagram hosting exotic spin nematic phases with highly entangled ground states near SU(3)-symmetric points. We use Tensor Renormalisation Group methods (e.g. graph—independent local truncation TRG) to study the phase diagram of the spin-1 bilinear biquadratic Heisenberg model with focus on the phase transitions near SU(3)-symmetric points. TRG methods are useful to study both non-critical and critical phases and give insight to new mechanisms of spin-nematic phases and exotic ground states.