Critical Level Crossings and Gapless Spin Liquid in the Square-Lattice Spin-1/2 J1-J2 Heisenberg Antiferromagnet

We use the density matrix renormalization group method to calculate several energy eigenvalues of the frustrated S=1/2 square-lattice J1-J2 Heisenberg model on 2L × L cylinders with L ≤ 10. We identify excited-level crossings versus the coupling ratio g=J2/J1 and study their drifts with the system size L. The lowest singlet-triplet and singlet-quintuplet crossings converge rapidly (with corrections ∝ L^−2) to different g values, and we argue that these correspond to ground-state transitions between the Neel antiferromagnet and a gapless spin liquid, at gc1≈0.46, and between the spin liquid and a valence-bond solid at gc2≈0.52. Previous studies of order parameters were not able to positively discriminate between an extended spin liquid phase and a critical point. We expect level-crossing analysis to be a generically powerful tool in density matrix renormalization group studies of quantum phase transitions.