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  • Title: Critical Level Crossings and Gapless Spin Liquid in the Square-Lattice Spin-1/2 J_{1}-J_{2} Heisenberg Antiferromagnet.
    Author: Wang L, Sandvik AW.
    Journal: Phys Rev Lett; 2018 Sep 07; 121(10):107202. PubMed ID: 30240235.
    Abstract:
    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×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 Néel antiferromagnet and a gapless spin liquid, at g_{c1}≈0.46, and between the spin liquid and a valence-bond solid at g_{c2}≈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.
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