Critical level crossings and gapless spin liquid in the square-lattice spin-1/2 J1-J2 Heisenberg antiferromagnet

Abstract

We use the DMRG method to calculate several energy eigenvalues of the frustrated S = 1 / 2 square-lattice J 1 - J 2 Heisenberg model on 2 L × L cylinders with L ≤ 10. We identify excited-level crossings versus the coupling ratio g = J 2 /J 1 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 N ́eel antiferromagnet and a gapless spin liquid, at g c 1 ≈ 0 . 46, and between the spin liquid and a valence-bond-solid at g c 2 ≈ 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 DMRG studies of quantum phase transitions.