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Arnaud Ralko, Didier Poilblanc and Roderich Moessner

The Rokhsar-Kivelson Quantum Dimer model (RK-QDM) on the square lattice, originally proposed in the context of high-temperature superconductivity, and its descendants have taken on a central role in the study of quantum systems incorporating a hard local constraint. They have thus been prominent in the context of hardcore bosons hopping on frustrated lattices, Josephson junction arrays, frustrated Ising models in a transverse field or with small XY exchange, gauge theories in unusual sectors, spin orbital models and cold atoms. Studies of this model and its extensions have unearthed a wealth of phenomena, including instances of deconfined quantum criticality and a new route to deconfinement.

As many RK models belong to the rare class of models of correlated quantum matter without a sign problem, they are in principle amenable to efficient numerical study ; they also tend to have well-studied effective field theories formulated in terms of height/gauge degrees of freedom.

In this work, we propose a generic alternative scenario to a first-order plaquette-columnar transition, as a continuous interpolation between them via a mixed phase (see Fig.1).

This we do by deriving from the dimer model a height model, with the height variable h, living on the plaquettes of the square lattice. Mutatis mutandis, such a mapping applies to d=2 RK models incorporating constraints which can be cast as local U(1) conservation laws. In this model, an ideal columnar phase has a mean value < h > equal to a half-integer, whereas an ideal plaquette phase has an integer < h >.

In this representation, the leading terms in an effective action incorporating all terms not ruled out by symmetry or microscopic considerations of the model in d=2+1 dimension are :

where denotes Euclidean time.

We find, depending on the value of the new term , a low-symmetry mixed state which continuously crosses over from primarily columnar to plaquette character (see Fig.1, central picture).

We also give a confirmation of the presence of this anisotropic scenario involving the mixed phase in the QDM on the square lattice, by the use of the Green’s function Monte-Carlo algorithm and symmetry considerations, applied for calculating the factor structure and the first gap excitation spectra for representative order parameters.

Post-scriptum :

Details and references are given in the corresponding paper "*Generic mixed columnar-plaquette phases in Rokhsar-Kivelson models*" published in :

A. Ralko, D. Poilblanc and R. Moessner, Physical Review Letters 100, 037201 (2008).

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