Potts-nematic Quantum Phase in Frustrated Heisenberg Anti-ferromagnets

In this talk we consider a class of quantum anti-ferromagnets with frustrated Heisenberg exchange interactions and collinear magnetic ground states which spontaneously break discrete lattice rotation symmetry. In particular, we examine the nature of the quantum phase transition between the disordered paramagnetic state and the magnetically ordered state, and show that this transition can occur via an intermediate paramagnetic phase in which rotation symmetry is broken. To demonstrate this, we investigate a spin-1 J₁-J₂ model on the triangular lattice with a single-ion anisotropy and show that the paramagnet becomes unstable to the formation of nematic two-particle bound states as the strength of the single-ion anisotropy decreases. This indicates the existence of a Potts-nematic quantum paramagnetic phase which lacks magnetic order, but breaks the three-fold rotation symmetry of the lattice. We also discuss generalizations to other systems and thermal phase transitions.