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Published July 17, 2013 | Submitted + Supplemental Material + Published
Journal Article Open

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

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.

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).

Attached Files

Published - PhysRevLett.111.037202.pdf

Submitted - 1301.4492v2.pdf

Supplemental Material - README.TXT

Supplemental Material - fig10.pdf

Supplemental Material - fig11.pdf

Supplemental Material - fig8.pdf

Supplemental Material - fig9.pdf

Supplemental Material - supplemental_v2.pdf

Supplemental Material - supplemental_v2.tex

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Additional details

Created:
August 19, 2023
Modified:
October 24, 2023