Starting from the mean-field solution of a spin-orbital model of $\mathrm{Li}\mathrm{Ni}{\mathrm{O}}_{2}$ , we derive an effective quantum dimer model (QDM) that lives on the triangular lattice and contains kinetic terms acting on four-site plaquettes and six-site loops. Using exact diagonalizations and Green's function Monte Carlo simulations, we show that the competition between these kinetic terms leads to a resonating valence bond (RVB) state for a finite range of parameters. We also show that this RVB phase is connected to the RVB phase identified in the Rokhsar-Kivelson model on the same lattice in the context of a generalized model that contains both the six-site loops and a nearest-neighbor dimer repulsion. These results suggest that the occurrence of an RVB phase is a generic feature of QDM with competing interactions.Starting from the mean-field solution of a spin-orbital model of $\mathrm{Li}\mathrm{Ni}{\mathrm{O}}_{2}$, we derive an effective quantum dimer model (QDM) that lives on the triangular lattice and contains kinetic terms acting on four-site plaquettes and six-site loops. Using exact diagonalizations and Green's function Monte Carlo simulations, we show that the competition between these kinetic terms leads to a resonating valence bond (RVB) state for a finite range of parameters. We also show that this RVB phase is connected to the RVB phase identified in the Rokhsar-Kivelson model on the same lattice in the context of a generalized model that contains both the six-site loops and a nearest-neighbor dimer repulsion. These results suggest that the occurrence of an RVB phase is a generic feature of QDM with competing interactions.

arXiv:cond-mat/0603633Physical Review BAug 2, 200637 citations

Quantum Dimer Model: Phase Diagrams

Garry Goldstein, Claudio Chamon, Claudio Castelnovo

Bulletin of the American Physical SocietyMar 14, 20160 citations

Minimal Models of Frustrated Quantum Magnets

Frédéric Mila

Frustrated quantum magnets are a real challenge to theorists because standard analytical and numerical methods fail in most cases.Significant progress has been recently achieved however on the basis of what one may call minimal models, i.e. models which keep at least one important aspect of frustration, but which are otherwise simple enough to be understood.In this paper, I will concentrate on two types of minimal models, Quantum Dimer Models and hard-core boson models.In the case of Quantum Dimer Models, I will review the evidence in favour of a Resonating Valence Bond (RVB) spin-liquid phase, and I will discuss under which circumstances such models might be good effective models.For hard-core boson models, which have been successfully used for quite some time for ladders and other non-frustrated models of coupled dimers, I will describe the specificities introduced by frustration (reduced kinetic energy, correlated hopping,...) and the unexpected properties they induce.Frustrated quantum magnets are a real challenge to theorists because standard analytical and numerical methods fail in most cases.Significant progress has been recently achieved however on the basis of what one may call minimal models, i.e. models which keep at least one important aspect of frustration, but which are otherwise simple enough to be understood.In this paper, I will concentrate on two types of minimal models, Quantum Dimer Models and hard-core boson models.In the case of Quantum Dimer Models, I will review the evidence in favour of a Resonating Valence Bond (RVB) spin-liquid phase, and I will discuss under which circumstances such models might be good effective models.For hard-core boson models, which have been successfully used for quite some time for ladders and other non-frustrated models of coupled dimers, I will describe the specificities introduced by frustration (reduced kinetic energy, correlated hopping,...) and the unexpected properties they induce.

AIP conference proceedingsJan 1, 20060 citations

Fractionalized Fermi liquids in a quantum dimer model

Junhyun Lee, Steven White, Subir Sachdev A

Bulletin of the American Physical SocietyMar 18, 20160 citations

Reduced density matrices and topological order in a quantum dimer model

Shunsuke Furukawa, Grégoire Misguich, Masaki Oshikawa

Resonating valence bond (RVB) liquids in two dimensions are believed to exhibit topological order and to admit no local order parameter of any kind. This is a defining property of "liquids" but it has been explicitly confirmed only in a few exactly solvable models. In this paper, we investigate the quantum dimer model on the triangular lattice. It possesses an RVB-type liquid phase, however, for which the absence of a local order parameter has not been proved. We examine the question numerically with a measure based on reduced density matrices. We find a scaling of the measure which strongly supports the absence of any local order parameter.Resonating valence bond (RVB) liquids in two dimensions are believed to exhibit topological order and to admit no local order parameter of any kind. This is a defining property of "liquids" but it has been explicitly confirmed only in a few exactly solvable models. In this paper, we investigate the quantum dimer model on the triangular lattice. It possesses an RVB-type liquid phase, however, for which the absence of a local order parameter has not been proved. We examine the question numerically with a measure based on reduced density matrices. We find a scaling of the measure which strongly supports the absence of any local order parameter.

arXiv:cond-mat/0607050Journal of Physics Condensed MatterMar 23, 20079 citations

Starting from the mean-field solution of a spin-orbital model of

\mathrm{Li}\mathrm{Ni}{\mathrm{O}}_{2}

, we derive an effective quantum dimer model (QDM) that lives on the triangular lattice and contains kinetic terms acting on four-site plaquettes and six-site loops. Using exact diagonalizations and Green's function Monte Carlo simulations, we show that the competition between these kinetic terms leads to a resonating valence bond (RVB) state for a finite range of parameters. We also show that this RVB phase is connected to the RVB phase identified in the Rokhsar-Kivelson model on the same lattice in the context of a generalized model that contains both the six-site loops and a nearest-neighbor dimer repulsion. These results suggest that the occurrence of an RVB phase is a generic feature of QDM with competing interactions.