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Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J_1−J_2 Square Heisenberg Model

Gong, Shou-Shu and Zhu, Wei and Sheng, D. N. and Motrunich, Olexei I. and Fisher, Matthew P. A. (2014) Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J_1−J_2 Square Heisenberg Model. Physical Review Letters, 113 (2). Art. No. 027201. ISSN 0031-9007. doi:10.1103/PhysRevLett.113.027201.

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We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J_1 and J_2, which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z_2 spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU (2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J_2 , we find a Néel phase and a plaquette valence-bond (PVB) phase with a finite spin gap. From the finite-size scaling of the magnetic order parameter, we estimate that the Néel order vanishes at J_2 /J _1 ≃0.44. For 0.5<J_2 /J_1 <0.61, we find dimer correlations and PVB textures whose decay lengths grow strongly with increasing system width, consistent with a long-range PVB order in the two-dimensional limit. The dimer-dimer correlations reveal the s -wave character of the PVB order. For 0.44<J_2 /J_1 <0.5, spin order, dimer order, and spin gap are small on finite-size systems, which is consistent with a near-critical behavior. The critical exponents obtained from the finite-size spin and dimer correlations could be compatible with the deconfined criticality in this small region. We compare and contrast our results with earlier numerical studies.

Item Type:Article
Related URLs:
URLURL TypeDescription Material Paper
Zhu, Wei0000-0003-4027-4711
Motrunich, Olexei I.0000-0001-8031-0022
Alternate Title:Plaquette ordered phase and quantum spin liquid in the spin-1/2 J_1-J_2 square Heisenberg model
Additional Information:© 2014 American Physical Society. Received 8 February 2014; Revised manuscript received 7 May 2014; Published 7 July 2014. We would like to particularly thank H.-C. Jiang and L. Balents for extensive discussions. We also acknowledge stimulating discussions with K. S. D. Beach, Z.-C. Gu, W.-J. Hu, L. Wang, S. White, Z.-Y. Zhu, and A. Sandvik. This research is supported by the National Science Foundation through Grants No. DMR-1205734 (S.-S. G.), No. DMR-0906816 (D. N. S.), No. DMR-1206096 (O. I.M.), No. DMR-1101912 (M. P. A. F.), the U.S. Department of Energy, Office of Basic Energy Sciences under Grant No. DE-FG02-06ER46305 (W. Z), and the Caltech Institute of Quantum Information and Matter, a NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation (O. I.M. and M. P. A. F.).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-06ER46305
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Issue or Number:2
Classification Code:PACS numbers: 73.43.Nq, 75.10.Jm, 75.10.Kt
Record Number:CaltechAUTHORS:20140714-131011965
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:47177
Deposited By: Joy Painter
Deposited On:14 Jul 2014 20:38
Last Modified:10 Nov 2021 17:36

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