Interacting classical dimers on the square lattice

Monte Carlo simulations and finite-size scaling theory have been used to study the critical behavior of repulsive dimers on square lattices at 2/3 monolayer coverage. A "zig-zag" (ZZ) ordered phase, characterized by domains of parallel ZZ strips oriented at $\pm 45^o$ from the lattice symmetry axes, was found. This ordered phase is separated from the disordered state by a order-disorder phase transition occurring at a finite critical temperature. Based on the strong axial ani...

For the inverse square long-range ferromagnetic Ising chain in a transverse field, the thermal phase boundary of the floating Kosterlitz-Thouless phase is obtained for several values of the transverse field down to the quantum critical point. The sharp domain walls in the classical model are increasingly smeared out by the transverse field, which is evidenced by a pronounced broadening of the non-universal bump in the specific heat. The discernability of KT critical scaling i...

The three-dimensional classical dimer model with interactions shows an unexpected continuous phase transition between an ordered dimer crystal and a Coulomb liquid. A detailed analysis of the critical dimer and monomer correlation functions point to a subtle interplay between the fluctuations of the crystal order parameter and the "magnetic" degrees of freedom present in the Coulomb phase. The distribution probability of the crystal order parameter suggests an emerging contin...

We study classical hard-core dimer models on the square lattice with links extending beyond nearest-neighbors. Numerically, using a directed-loop Monte Carlo algorithm, we find that, in the presence of longer dimers preserving the bipartite graph structure, algebraic correlations persist. While the confinement exponent for monomers drifts, the leading decay of dimer correlations remains 1/r^2, although the logarithmic peaks present in the dimer structure factor of the nearest...

We determine the dynamical dimer correlation functions of quantum dimer models at the Rokhsar-Kivelson point on the bipartite square and cubic lattices and the non-bipartite triangular lattice. Based on an algorithmic idea by Henley, we simulate a stochastic process of classical dimer configurations in continuous time and perform a stochastic analytical continuation to obtain the dynamical correlations in momentum space and the frequency domain. This approach allows us to obs...

We present an unbiased numerical density-matrix renormalization group study of the one-dimensional Bose-Hubbard model supplemented by nearest-neighbor Coulomb interaction and bond dimerization. It places the emphasis on the determination of the ground-state phase diagram and shows that, besides dimerized Mott and density-wave insulating phases, an intermediate symmetry-protected topological Haldane insulator emerges at weak Coulomb interactions for filling factor one, which d...

We study the nature of the ground state of the quantum dimer model proposed by Rokhsar and Kivelson by diagonalizing the Hamiltonian of the model on square lattices of size $L\times L$, where $L\leq 8$, with periodic boundary conditions. Finite-size scaling studies of the columnar order parameter and the low lying excitation spectrum show no evidence of a dimer liquid state in any finite region of the zero temperature phase diagram. In addition, we find evidence of a transiti...

We analyze classical dimer models on the square and triangular lattice using a tensor network representation of the dimers. The correlation functions are numerically calculated using the recently developed "Tensor renormalization group" (TRG) technique. The partition function for the dimer problem can be calculated exactly by the Pfaffian method which is used here as a platform for comparing the numerical results. TRG turns out to be a powerful tool for describing gapped syst...

An efficient Monte Carlo algorithm for the simulation of spin models with long-range interactions is discussed. Its central feature is that the number of operations required to flip a spin is independent of the number of interactions between this spin and the other spins in the system. In addition, critical slowing down is strongly suppressed. In order to illustrate the range of applicability of the algorithm, two specific examples are presented. First, some aspects of the Ko...

A highly efficient and simple to implement Monte Carlo algorithm is proposed for the evaluation of the Renyi entanglement entropy(REE) of quantum dimer model(QDM) at the Rokhsar-Kivelson(R-K) point. It makes possible the evaluation of REE at the R-K point to the thermodynamic limit for a general QDM. We apply the algorithm to QDM on both triangular and square lattice as demonstrations and find the REE on both lattices follow perfect linear scaling in the thermodynamic limit, ...