Quantum phase transitions in the two-dimensional J₁-J₂ model

We analyze the phase diagram of the frustrated Heisenberg antiferromagnet, the J₁-J₂ model, in two dimensions. Two quantum phase transitions in the model are already known: the second-order transition from the Néel state to the spin liquid state at (J₂/J₁)_c2≈0.38, and the first-order transition from the spin liquid state to the collinear state at (J₂/J₁)_c4≈0.60. We have found evidence for two second-order phase transitions: the transition from the spin columnar dimerized state to the state with plaquette-type modulation at (J₂/J₁)_c3=0.50±0.02, and the transition from the simple Néel state to the Néel state with spin columnar dimerization at (J₂/J₁)_c1=0.34±0.04. We also present an independent calculation of (J₂/J₁)_c2≈0.38 using another approach.