Quantum phase transitions in the two-dimensionalJ1−J2model

We analyze the phase diagram of the frustrated Heisenberg antiferromagnet, the $J_1{-J}_2$ 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 ${(J}_2{/J}_1{)}_{c2\mathrm{}}\approx 0.38,$ and the first-order transition from the spin liquid state to the collinear state at ${(J}_2{/J}_1{)}_{c4\mathrm{}}\approx \mathrm{0.60.}$ 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 ${(J}_2{/J}_1{)}_{c3\mathrm{}}=0.50\mathrm{}\pm 0.02,$ and the transition from the simple Néel state to the Néel state with spin columnar dimerization at ${(J}_2{/J}_1{)}_{c1\mathrm{}}=0.34\mathrm{}\pm \mathrm{0.04.}$ We also present an independent calculation of ${(J}_2{/J}_1{)}_{c2\mathrm{}}\approx 0.38$ using another approach.