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Constructing a Gapless Spin-Liquid State for the Spin-1/2 J_1-J_2 Heisenberg Model on a Square Lattice

Wang, Ling and Poilblanc, Didier and Gu, Zheng-Cheng and Wen, Xiao-Gang and Verstraete, Frank (2013) Constructing a Gapless Spin-Liquid State for the Spin-1/2 J_1-J_2 Heisenberg Model on a Square Lattice. Physical Review Letters, 111 (3). Art. No. 037202. ISSN 0031-9007. https://resolver.caltech.edu/CaltechAUTHORS:20130910-102434559

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Abstract

We construct a class of projected entangled pair states which is exactly the resonating valence bond wave functions endowed with both short range and long range valence bonds. With an energetically preferred resonating valence bond pattern, the wave function is simplified to live in a one-parameter variational space. We tune this variational parameter to minimize the energy for the frustrated spin-1/2 J_1-J_2 antiferromagnetic Heisenberg model on the square lattice. Taking a cylindrical geometry, we are able to construct four topological sectors with an even or odd number of fluxes penetrating the cylinder and an even or odd number of spinons on the boundary. The energy splitting in different topological sectors is exponentially small with the cylinder perimeter. We find a power law decay of the dimer correlation function on a torus, and a lnL correction to the entanglement entropy, indicating a gapless spin-liquid phase at the optimum parameter.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1301.4492arXivDiscussion Paper
http://dx.doi.org/10.1103/PhysRevLett.111.037202 DOIArticle
http://link.aps.org/doi/10.1103/PhysRevLett.111.037202PublisherArticle
Additional Information:© 2013 American Physical Society. Received 5 February 2013; revised manuscript received 25 June 2013; published 17 July 2013. We would also like to thank N. Schuch, I. Cirac, D. Perez-Garcia, and O. Motrunich for stimulating discussions. This project is supported by the EU Strep project QUEVADIS, the ERC grant QUERG, the FWF SFB grants FoQuS and ViCoM, and the NQPTP ANR-0406-01 grant (French Research Council). X. G.W. is supported by NSF Grants No. DMR-1005541, No. NSFC 11074140, and No. NSFC 11274192. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research. The computational results presented have been achieved using the Vienna Scientific Cluster (VSC) and the CALMIP Hyperion Cluster (Toulouse).
Funders:
Funding AgencyGrant Number
EU Strep Project QUEVADISUNSPECIFIED
ERC Grant QUERGUNSPECIFIED
FWF SFB Grant FoQuSUNSPECIFIED
FWF SFB Grant ViCoMUNSPECIFIED
French Research CouncilNQPTP ANR-0406-01
NSFDMR-1005541
NSFC11074140
NSFC11274192
Government of CanadaUNSPECIFIED
Industry CanadaUNSPECIFIED
Province of Ontario Ministry of ResearchUNSPECIFIED
Issue or Number:3
Classification Code:PACS: 75.10.Kt, 75.10.Jm
Record Number:CaltechAUTHORS:20130910-102434559
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130910-102434559
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41204
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Sep 2013 22:03
Last Modified:03 Oct 2019 05:46

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