期刊
PHYSICAL REVIEW LETTERS
卷 121, 期 10, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.121.107202
关键词
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资金
- National Key Research and Development program of China [2016YFA0300603]
- National Natural Science Foundation of China [NSFC-11734002, NSFC-11474016]
- National Thousand Young Talents Program of China
- NSAF Program of China [U1530401]
- NSF [DMR-1410126, DMR-1710170]
- Simons Investigator Grant
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.
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