Thermal Phase Transitions in the J₁-J₂ Heisenberg Model

The spin-1/2 Heisenberg model on the square lattice with nearest-neighbor coupling J₁ and next-nearest coupling J₂ (J₁-J₂ model) has imposed itself as a paradigmatic model of frustrated quantum magnetism. Beyond its theoretical relevance, this model is experimentally realized in various vanadium oxides with a wide range of J₂/J₁ values. It also attracted attention as an effective model to describe the magnetic properties of iron-based superconductors.

Despite its significance and extensive theoretical scrutiny, this model presents a formidable challenge for numerical simulation. Quantum Monte Carlo simulations, in particular, grapple with very serious minus sign problem. At finite temperature, the main open question concerns the possibility of an Ising transition at finite temperature in the collinear phase, as predicted in 1990 by Chandra, Coleman, and Larkin.

We investigate the model using a state of the art tensor network approach. Employing an SU(2) invariant Projected Entangled Pair States (PEPS) algorithm, we expose the first unambiguous and direct evidence of a thermal Ising transition associated with the spontaneous breaking of C_4v symmetry within the collinear antiferromagnet region of the phase diagram. We also consider the ferromagnetic (J₁ > 0) case and draw its complete finite temperature phase diagram, including the first order transition and the two critical points appearing in the intermediate region.