We study the transition between a Coulomb phase and a dimer crystal observed in numerical simulations of the three-dimensional classical dimer model, by mapping it to a quantum model of bosons in two dimensions. The quantum phase transition that results, from a superfluid to a Mott insulator at fractional filling, belongs to a class that cannot be described within the Landau-Ginzburg-Wilson paradigm. Using a second mapping, to a dual model of vortices, we show that the long-wavelength physics near the transition is described by a U(1) gauge theory with SU(2) matter fields.
We study a model of hard-core bosons on the kagome lattice with short-range hopping
(t) and repulsive interactions
(V). This model directly maps onto an easy-axis
S=1∕2 XXZ model on the kagome lattice and is also related, at large
V∕t, to a quantum dimer model on the triangular lattice. Using quantum Monte Carlo numerics, we map out the phase diagram of this model at half-filling. At
T=0, we show that this model exhibits a superfluid phase at small
V∕t and an insulating phase at large
V∕t, separated by a continuous quantum phase transition at ${V}_{c}∕t\ensuremath{\approx}19.8$. The insulating phase at
T=0 appears to have no conventional broken symmetries, and is thus a uniform Mott insulator (a ``spin liquid'' in magnetic language). We characterize this insulating phase as a uniform
Z2 fractionalized insulator from the topological order in the ground state and estimate its vison gap. Consistent with this identification, there is no apparent thermal phase transition upon heating the insulator. The insulating phase instead smoothly crosses over into the high temperature paramagnet via an intermediate cooperative paramagnetic regime. We also study the superfluid-to-normal thermal transition for
V<Vc. We find that this is a Kosterlitz-Thouless transition at small
V∕t but changes to a first order transition for
V closer to
Vc. We argue that this first order thermal transition is consistent with the presence of a nearby
Z2 insulating ground state obtained from the superfluid ground state by condensing double vortices.
We consider the
(2+1)-dimensional
SU(2) quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges [which transform nontrivially under the
Z(2) center of the
SU(2) gauge group] are confined to each other by fractionalized strings with a delocalized
Z(2) flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the three-dimensional Ising universality class separates two confining phases: one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.
We study the classical cubic-lattice double dimer model, consisting of two coupled replicas of the close-packed dimer model, using a combination of theoretical arguments and Monte Carlo simulations. Our results establish the presence of a ``synchronization transition'' at a critical value of the coupling, where both replicas remain disordered but their fluctuations become strongly correlated. We show that this unconventional transition, which has neither external nor spontaneous symmetry breaking, is continuous and belongs to the three-dimensional inverted-XY universality class. By adding aligning interactions for dimers within each replica, we map out the full phase diagram, including the interplay between columnar ordering and synchronization. We also solve the coupled double dimer model exactly on the Bethe lattice and show that it correctly reproduces the qualitative phase structure but with mean-field critical behavior.
We use large scale quantum Monte Carlo simulations to study an extended Hubbard model of hard core bosons on the kagome lattice. In the limit of strong nearest-neighbor interactions at 1/3 filling, the interplay between frustration and quantum fluctuations leads to a valence bond solid ground state. The system undergoes a quantum phase transition to a superfluid phase as the interaction strength is decreased. It is still under debate whether the transition is weakly first order or represents an unconventional continuous phase transition. We present a theory in terms of an easy plane noncompact CP^{1} gauge theory describing the phase transition at 1/3 filling. Utilizing large scale quantum Monte Carlo simulations with parallel tempering in the canonical ensemble up to 15552 spins, we provide evidence that the phase transition is continuous at exactly 1/3 filling. A careful finite size scaling analysis reveals an unconventional scaling behavior hinting at deconfined quantum criticality.
We examine the equilibrium properties of lattice bosons with attractive on-site interactions in the presence of a three-body hard-core constraint that stabilizes the system against collapse and gives rise to a dimer superfluid phase. Employing quantum Monte Carlo simulations, the ground state phase diagram of this system on the square lattice is analyzed. In particular, we study the quantum phase transition between the atomic and dimer superfluid regime and analyze the nature of the superfluid-insulator transitions. Evidence is provided for the existence of a tricritical point along the saturation transition line, where the transition changes from being first order to a continuous transition of the dilute Bose gas of holes. The Berzinskii-Kosterlitz-Thouless transition from the dimer superfluid to the normal fluid is found to be consistent with an anomalous stiffness jump, as expected from the unbinding of half-vortices.