Critical Level Crossings and Gapless Spin Liquid in the Square-Lattice Spin-1/2 J_1-J_2 Heisenberg Antiferromagnet

摘要

We use the density matrix renormalization group method to calculate several energy eigenvalues of the frustrated S = 1/2 square-lattice J(1) - J(2) Heisenberg model on 2L x 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 alpha 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 g(c1) approximate to 0.46, and between the spin liquid and a valence-bond solid at g(c2) approximate to 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.