Related papers: A quantum monomer-dimer model on Penrose tilings
Simulations in finite density, beta=0 lattice QCD by means of the Monomer-Dimer-Polymer algorithm show a signal of first order transition at finite temporal size. This behaviour agrees with predictions of the mean field approximation, but…
Finite-temperature phase transitions in quasi-one-dimensional quarter-filled systems are investigated by the extended Hubbard model with electron-lattice coupling. Using a quantum Monte Carlo method combined with the inter-chain mean-field…
We construct a quantum extension of the (classical) three-coloring model introduced by Baxter [J.Math.Phys.11, 784 (1970)] for which the ground state can be computed exactly along a continuous line of Rokhsar-Kivelson solvable points. The…
Quantum link models (QLMs) are generalizations of Wilson's lattice gauge theory formulated with finite-dimensional link Hilbert spaces. In certain cases, the non-Abelian Gauss Law constraint can be exactly solved, and the gauge invariant…
This note relates topics in statistical mechanics, graph theory and combinatorics, lattice quantum field theory, super quantum mechanics and string theory. We give a precise relation between the dimer model on a graph embedded on a torus…
Using the density matrix renormalization group (DMRG) method, we study the quantum coherence in one-dimensional disordered Fermi systems. We consider in detail spinless fermions on a ring, and compare the influence of several kinds of…
We study classical dimers on two-dimensional quasiperiodic Ammann-Beenker (AB) tilings. Despite the lack of periodicity we prove that each infinite tiling admits 'perfect matchings' in which every vertex is touched by one dimer. We…
We consider a quantum dimer model (QDM) on the kagome lattice which was introduced recently [Phys. Rev. Lett. 89, 137202 (2002)]. It realizes a Z_2 liquid phase and its spectrum was obtained exactly. It displays a topological degeneracy…
We construct a non-commutative scheme that behaves as if it is the space of Penrose tilings of the plane. Let k be a field and B=k<x,y>(y^2). We consider B as the homogeneous coordinate ring of a non-commutative projective scheme. The…
Motivated by phenomenological models of hidden local symmetries and the ideas of dimensional deconstruction and gauge/gravity duality, we consider the model of an "open moose". Such a model has a large number K of hidden gauge groups as…
A square-lattice hard-core dimer model with links extending beyond nearest-neighbors is studied using a directed-loop Monte Carlo method. An arbitrarily small fraction of next-nearest-neighbor dimers is found to cause deconfinement, whereas…
We study and solve the ground-state problem of a microscopic model for a family of orbitally degenerate quantum magnets. The orbital degrees of freedom are assumed to have directional character and are represented by static Potts-like…
We present results from extensive Monte Carlo simulations of polymer models where each lattice site can be visited by up to $K$ monomers and no restriction is imposed on the number of bonds on each lattice edge. These \textit{multiple…
We study the correlations of classical hardcore dimer models doped with monomers by Monte Carlo simulation. We introduce an efficient cluster algorithm, which is applicable in any dimension, for different lattices and arbitrary doping. We…
We explore the ground-state physics of two-dimensional spin-$1/2$ $U(1)$ quantum link models, one of the simplest non-trivial lattice gauge theories with fermionic matter within experimental reach for quantum simulations. Whereas in the…
Two-dimensional Rokhsar-Kivelson (RK) dimer models on bipartite lattices are generally limited to translation-symmetry-broken dimer crystals. We introduce a tensor-product regularisation of the dimer Hilbert space that yields a qubit…
We study the transverse-field Ising model on a square lattice with bond- and site-dilution at zero temperature by stochastic series expansion quantum Monte Carlo simulations. Tuning the transverse field $h$ and the dilution $p$, the quantum…
A set of simple rules for constructing the maximal (e.g. analytic) extensions for any metric with a Killing field in an (effectively) two-dimensional spacetime is formulated. The application of these rules is extremely straightforward, as…
Recently, quantum dimer models, in which the system can tunnel between different classical dimer configurations, have attracted a great deal of interest as a paradigm for the study of exotic quantum phases. Much of this excitement has…
A two-dimensional spin-up ideal Fermi gas interacting attractively with a spin-down impurity in the continuum undergoes, at zero temperature, a first-order phase transition from a polaron to a dimeron state. Here we study a similar system…