Quantum Dimer Model: Phase Diagrams

Zheng Yan, Zheng Zhou, Olav F. Syljuåsen +4 more

Tommaso Coletta, Jean-David Picon, S. E. Korshunov +1 more

Motivated by the current interest in the quantum dimer model on the triangular lattice, we investigate the phase diagram of the closely related fully frustrated transverse-field Ising model on the honeycomb lattice using classical and semiclassical approximations. We show that, in addition to the fully polarized phase at a large field, the classical model possesses a multitude of phases that break the translational symmetry which, in the dimer language, correspond to a plaquette phase and a columnar phase separated by an infinite cascade of mixed phases. The modification of the phase diagram by quantum fluctuations has been investigated in the context of linear spin-wave theory. The extrapolation of the semiclassical energies suggests that the plaquette phase extends down to zero field for spin 1/2, in agreement with the $\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}$ phase of the quantum dimer model on the triangular lattice with only kinetic energy.

Roderich Moessner, Kumar S. Raman

Anasuya Kundu, Swapan Kumar Pati

We investigate the phase diagram of a dimerized Bose-Hubbard model, using a density matrix renormalization group technique. We find a new phase, which is the coexistence of superfluid and bond-wave phases, due to the effect of dimerization. Experimentally dimerization in optical lattice can be realized by using two counterpropagating laser beams of different wavelengths. Apart from the conventional superfluid–to–Mott-insulator transition, we find a new quantum phase transition: from superfluid-bond-wave to Mott-insulator-bond wave phase. Our study suggests a rich phase diagram which can be easily probed.

Thiago Milanetto Schlittler, Thomas Barthel, Grégoire Misguich +2 more

We introduce a quantum dimer model on the hexagonal lattice that, in addition to the standard three-dimer kinetic and potential terms, includes a competing potential part counting dimer-free hexagons. The zero-temperature phase diagram is studied by means of quantum Monte Carlo simulations, supplemented by variational arguments. It reveals some new crystalline phases and a cascade of transitions with rapidly changing flux (tilt in the height language). We analyze perturbatively the vicinity of the Rokhsar-Kivelson point, showing that this model has the microscopic ingredients needed for the "devil's staircase" scenario [Eduardo Fradkin et al. Phys. Rev. B 69, 224415 (2004)], and is therefore expected to produce fractal variations of the ground-state flux.

Johannes Feldmeier, Michael Knap, Frank Pollmann