Constructing a Gapless Spin-Liquid State for the Spin-1/2 J1J2 Heisenberg Model on a Square Lattice

Ling Wang, Didier Poilblanc, Zheng-Cheng Gu, Xiao-Gang Wen, and Frank Verstraete
Phys. Rev. Lett. 111, 037202 – Published 17 July 2013
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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 J1J2 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.

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  • Received 5 February 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.037202

© 2013 American Physical Society

Authors & Affiliations

Ling Wang1,2, Didier Poilblanc3, Zheng-Cheng Gu2, Xiao-Gang Wen4,5,6, and Frank Verstraete1,7

  • 1Faculty of Physics, Vienna Center for Quantum Science and Technology, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
  • 2Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
  • 3Laboratoire de Physique Théorique, C.N.R.S. and Université de Toulouse, 31062 Toulouse, France
  • 4Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada
  • 5Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 6Institute for Advanced Study, Tsinghua University, Beijing 100084, People’s Republic of China
  • 7Faculty of Physics and Astronomy, University of Ghent, Krijgslaan 281 S9, B-9000 Ghent, Belgium

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Issue

Vol. 111, Iss. 3 — 19 July 2013

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