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Tensor-product state approach to spin-1/2 square J_1−J_2 antiferromagnetic Heisenberg model: Evidence for deconfined quantum criticality

Wang, Ling and Gu, Zheng-Cheng and Verstraete, Frank and Wen, Xiao-Gang (2016) Tensor-product state approach to spin-1/2 square J_1−J_2 antiferromagnetic Heisenberg model: Evidence for deconfined quantum criticality. Physical Review B, 94 (7). Art. No. 075143. ISSN 2469-9950. https://resolver.caltech.edu/CaltechAUTHORS:20160824-082741487

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Abstract

The ground state phase of a spin-1/2 J_1−J_2 antiferromagnetic Heisenberg model on a square lattice around the maximally frustrated regime (J_2∼0.5J_1) has been debated for decades. Here we study this model using the cluster update algorithm for tensor-product states (TPSs). The ground state energies at finite sizes and in the thermodynamic limit (with finite size scaling) are in good agreement with exact diagonalization study. Through finite size scaling of the spin correlation function, we find the critical point J^(c1)_2 = 0.572(5)J_1 and critical exponents ν = 0.50(8), η_s = 0.28(6). In the range of 0.572 < J_2/J_1 ≤ 0.6 we find a paramagnetic ground state with an exponentially decaying spin-spin correlation. Up to a 24×24 system size, we observe power law decaying dimer-dimer and plaquette-plaquette correlations with an anomalous plaquette scaling exponent η_p = 0.24(1) and an anomalous columnar scaling exponent η_c = 0.28(1) at J_2/J_1 = 0.6. These results are consistent with a potential gapless U(1) spin-liquid phase. However, since the U(1) spin liquid is unstable due to the instanton effect, a valence bond solid order with very small amplitude might develop in the thermodynamic limit. Thus, our numerical results strongly indicate a deconfined quantum critical point at J^(c1)_2. Remarkably, all the observed critical exponents are consistent with the J−Q model.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevB.94.075143DOIArticle
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.94.075143PublisherArticle
https://arxiv.org/abs/1112.3331arXivDiscussion Paper
Alternate Title:A tensor product state approach to spin-1/2 square J1-J2 antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
Additional Information:© 2016 American Physical Society. Received 24 May 2016; published 19 August 2016. We would like to thank J. Richter for passing along their exact diagonalization data for comparison, F. Becca for passing along their variational Monte Carlo data for comparison, and A. W. Sandvik, Leon Balents, H.-C. Jiang, D. Sheng, S.-S. Gong, and Z.-Y. Zhu for their stimulating discussions. L.W. is supported by National Natural Science Foundation of China (NSFC-11474016), National Thousand Young Talents program of China. Z.C.G. is supported by startup support from Department of Physics, CUHK. F.V. is supported by the EU Strep Project QUEVADIS, the ERC Grant QUERG, and the FWF SFB Grants FoQuS and ViCoM. The computational results presented have been achieved partially using Tianhe- 2JK computing time award at the Beijing Computational Science Research Center (CSRC).
Group:Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
National Natural Science Foundation of ChinaNSFC-11474016
National Thousand Young Talents program of ChinaUNSPECIFIED
European UnionUNSPECIFIED
European Research Council (ERC)UNSPECIFIED
FWF Der WissenschaftsfondsUNSPECIFIED
Issue or Number:7
Record Number:CaltechAUTHORS:20160824-082741487
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160824-082741487
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69884
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:24 Aug 2016 17:04
Last Modified:03 Oct 2019 10:26

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