Semiclassical Analysis of Quantum Dimer Models

ORAL

Abstract

We use the slave boson approach to develop the semiclassical description of the Rokshar Kivelson square lattice quantum dimer model, which allows a 1/S expansion. The action reproduces a generalized height representation. We extend these results to the dimer model on the cubic lattice, where we obtain emergent quantum electrodynamics description. The estimated speed of light: c = S/2*Sqrt[(J−V)J]. We confirm aspects of the height mapping such as the correlation between the sign of the terms in the height action and the sign of the potential term in the RK Hamiltonian. In dimensions D = 2, 3 the QED emerges at wave vectors (π,π) and (π,π,π) respectively. Our estimate of the RK parameter is 1/16 which is within a 20 to 30 percent of the exact value of 1/4π. We extend our analysis to the hexagonal and diamond lattices, and we find that the speed of light for the diamond lattice is given by c^2 = S^4*[(J − V )J]/64.

*A.M.T. is supported by the Condensed Matter Physics and Materials Science Division, in turn funded by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. DESC0012704. This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) Grant No. EP/M007065/1 (C.C. and G.G.) and by NSF grant No. DMR-1733071 (G.G.)

–

Presenters

  • Garry Goldstein

    • Rutgers University
    • Physics, Rutgers University

Authors

  • Garry Goldstein

    • Rutgers University
    • Physics, Rutgers University

  • Claudio Castelnovo

    • Cavendish Laboratory, University of Cambridge
    • TCM, University of Cambridge
    • Dept of Physics, University of Cambridge
    • University of Cambridge
    • Physics, Cambridge University

  • Gabriel Kotliar

    • Rutgers University and Brookhaven National Laboratories
    • Department of Condensed Matter Physics and Materials Science, Upton, New York 11973, USA, Brookhaven National Laboratory
    • Rutgers University, New Brunswick
    • Brookhaven National Laboratory
    • Department of Physics, Rutgers University
    • Physics, Rutgers University
    • Rutgers University, New Jersey, USA
    • Physics and Astronomy Department, Rutgers University
    • Department of Physics and Astronomy, Rutgers University, NJ

  • Alexei Tsvelik

    • Physics, Brook Haven National Laboratory