In this paper, we investigate if it occurs a phase transition for a system of classical dimers adsorbed on a 3-4 lattice in the thermodynamic limit. We define four types of bonds (denoted by the dimers activities adsorbed in her, $x$, $y$, $u$ and $v$) and evaluated the partition function from the combinatorial method of the pfaffian and using periodic boundary conditions. We write the density of free energy per particle and the condition to his analyticity, showing that there is a critical point for a determined choice of the activities. We also numerically evaluated the integral on free energy and their derivates (entropy and specific heat) for the same case and compute the entropy density and molecular freedom per particle at high temperatures for this choice of the activities.
We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decorated square lattice perturbed by two kinds of further neighbor couplings. In our previous study [J. Phys. Soc. Jpn. 85, 094002 (2016)], the second-order effective Hamiltonian for the Heisenberg model perturbed by a further neighbor coupling was found to be a square-lattice quantum-dimer model with a finite hopping amplitude, t>0, and no dimer-dimer interaction, v=0. In this study, we introduce another kind of further neighbor coupling and show that it leads to an attractive interaction between dimers, which suggests the stabi…
We discuss the exact solutions of various models of the statistics of dimer coverings of a Bethe lattice. We reproduce the well-known exact results for noninteracting hard-core dimers by both a very simple geometrical argument and a general algebraic formulation for lattice statistical problems. For the Bethe lattice we also obtain the exact solution when either a) the dimers interact via a short-range interaction or b) the underlying lattice is anisotropic. We also give solutions for special cases of random lattices and for the jamming limit of one dimensional deposition of dimers.
We study the mechanism of loop condensation in the quantum dimer model on the triangular lattice. The triangular lattice quantum dimer model displays a topologically ordered quantum liquid phase in addition to conventionally ordered phases with broken symmetry. In the context of systems with extended loop-like degrees of freedom, the formation of such topological order can be described in terms of loop condensation. Using Monte Carlo calculations with local and directed-loop updates, we compute geometric properties of the transition graph loop distributions of several triangular lattice quantu…
We study the model of close-packed dimers on planar lattices belonging to the family of modified rectangular (MR) fractals, whose members are enumerated by an integer $p\geq 2$, as well as on the non-planar 4-simplex fractal lattice. By applying an exact recurrence enumeration method, we determine the asymptotic forms for numbers of dimer coverings, and numerically calculate entropies per dimer in the thermodynamic limit, for a sequence of MR lattices with $2\leq p\leq8$ and for 4-simplex fractal. We find that the entropy per dimer on MR fractals is increasing function of the scaling parameter…
We construct a class of lattices in three and higher dimensions for which the number of dimer coverings can be determined exactly using elementary arguments. These lattices are a generalization of the two-dimensional kagome lattice, and the method also works for graphs without translational symmetry. The partition function for dimer coverings on these lattices can be determined also for a class of assignments of different activities to different edges.
Random sequential adsorption (RSA) is a standard method of modeling adsorption of large molecules at the liquid-solid interface. Here we consider jammed states of the RSA process of nonoverlapping dimers (objects occupying two nearest-neighbor lattice sites) in a hypercubic lattice of arbitrary space dimension $D \ge 2$. We show that each dimer in such a state belongs to a percolating cluster.
A star-triangle mapping transformation is used to establish an exact correspondence between the spin-1/2 Ising model on the Shastry-Sutherland (orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a bathroom tile (4-8) lattice. Exact results for the critical temperature and spontaneous magnetization are obtained and compared with corresponding results on the regular Ising lattices.
We study vacancy diffusion on the classical triangular lattice dimer model, sub ject to the kinetic constraint that dimers can only translate, but not rotate. A single vacancy, i.e. a monomer, in an otherwise fully packed lattice, is always localized in a tree-like structure. The distribution of tree sizes is asymptotically exponential and has an average of 8.16 \pm 0.01 sites. A connected pair of monomers has a finite probability of being delocalized. When delocalized, the diffusion of monomers is anomalous:
Covering a graph or a lattice with non-overlapping dimers is a problem that has received considerable interest in areas such as discrete mathematics, statistical physics, chemistry and materials science. Yet, the problem of percolation on dimer-covered lattices has received little attention. In particular, percolation on lattices that are fully covered by non-overlapping dimers has not evidently been considered. Here, we propose a novel procedure for generating random dimer coverings of a given lattice. We then compute the bond percolation threshold on random and ordered coverings of the squar…
Using the tensor network approach, we investigate the monomer-dimer models on a checkerboard lattice, in which there are interactions (with strength $ν$) between the parallel dimers on half of the plaquettes. For the fully packed interacting dimer model, we observe a Kosterlitz-Thouless (KT) transition between the lowtemperature symmetry breaking and the high-temperature critical phases; for the doped monomer-dimer casewith finite chemical potential $μ$, we also find an order-disorder phase transition which is of second order instead. We use the boundary matrix product state approach to detect…
Behavior of the mixture of particles and dimers moving with different jump rates at reconstructed surfaces is described. Collective diffusion coefficient is calculated by the variational approach. Anisotropy of the collective particle motion is analyzed as a function of jump rates and local particle density. Analytic expressions are compared with the results of Monte Carlo simulations of diffusing particle and dimer mixture. Direction of driven diffusive motion of the same system depends on the jump anisotropy and on the value of driving force. Driven motion results in the particle and dimer s…
In recent work the author presented a formal expansion for lambda_d associated to the dimer problem on a d-dimensional rectangular lattice. Expressed in terms of d it yielded a presumed asymptotic expansion for lambda_d in inverse powers of d. We also considered an expansion in powers of x, a formal variable ultimately set equal to 1. We believe this series has better asymptotic properties than the expansion in inverse powers of d. We discuss this, and apply the same method to the two-dimensional triangular and hexagonal lattices. Viewed as a test of the x-expansion the results on those two la…
We analyze the partition function of the dimer model on an $\mathcal{M} \times \mathcal{N}$ triangular lattice wrapped on torus obtained by Fendley, Moessner and Sondhi [Phys. Rev. B \textbf{66}, 214513 (2002)]. From a finite-size analysis we have found that the dimer model on such a lattice can be described by conformal field theory having central charge $c=1$. The shift exponent for the specific heat is found to depend on the parity of the number of lattice sites $\mathcal{N}$ along a given lattice axis: e.g., for odd $\mathcal{N}$ we obtain the shift exponent $λ=1$, while for even $\mathcal…
We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decorated square lattice. The diamond-like-decorated square lattice is a lattice in which the bonds in a square lattice are replaced with diamond units. The diamond unit has two types of antiferromagnetic exchange interactions, and the ratio $λ$ of the diagonal bond strength to that of the other four edges controls the frustration strength. For $0.974<λ<2$, the present system has a nontrivial macroscopic degeneracy, which is called the macroscopically degenerated tetramer-dimer (MDTD) states. The MDTD states are identical to the H…
Exact analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer interactions. We show that both models are equivalent to a 5-vertex model on the square lattice with interlayer vertex-vertex interactions. Using the method of Bethe ansatz, a closed-form expression for the free energy is obtained and analyzed. We deduce the exact phase diagram and determine the nature of the phase transitions as a function of the strength of the…
Lattice models are useful for understanding behaviors of interacting complex many-body systems. The lattice dimer model has been proposed to study the adsorption of diatomic molecules on a substrate. Here we analyze the partition function of the dimer model on an $2 M \times 2 N$ checkerboard lattice wrapped on a torus and derive the exact asymptotic expansion of the logarithm of the partition function. We find that the internal energy at the critical point is equal to zero. We also derive the exact finite-size corrections for the free energy, the internal energy, and the specific heat. Using …
We study a monomer-dimer mixture defined on a honeycomb lattice as a toy model for the spin ice system in a magnetic field. In a low-doping region of monomers, the effective description of this system is given by the dual sine-Gordon model. In intermediate- and strong-doping regions, the Potts lattice gas theory can be employed. Synthesizing these results, we construct a renormalization-group flow diagram, which includes the stable and unstable fixed points corresponding to ${\cal M}_5$ and ${\cal M}_6$ in the minimal models of the conformal field theory. We perform numerical transfer-matrix c…
We present a numerical study on an interacting monomer-dimer model with nearest neighbor repulsion on a square lattice, which possesses two symmetric absorbing states. The model is observed to exhibit two nearby continuous transitions: the $Z_2$ symmetry-breaking order-disorder transition and the absorbing transition with directed percolation criticality. We find that the symmetry-breaking transition shows a non-Ising critical behavior, and that the absorbing phase becomes critical, in the sense that the critical decay of the dimer density observed at the absorbing transition persists even wit…
Analytical solutions for the time-dependent autocorrelation function of the classical and quantum mechanical spin dimer with arbitrary spin are presented and compared. For large spin quantum numbers or high temperature the classical and the quantum dimer become more and more similar, yet with the major difference that the quantum autocorrelation function is periodic in time whereas the classical is not.
We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid-Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.
We report on simulations of reversible random sequential adsorption of dimers on three different lattices: a one-dimensional lattice, a two-dimensional triangular lattice, and a two-dimensional triangular lattice with the nearest neighbors excluded. In addition to the adsorption of particles at a rate K+, we allow particles to leave the surface at a rate K-. The results from the one-dimensional lattice model agree with previous results for the continuous parking lot model. In particular, the long-time behavior is dominated by collective events involving two particles. We were able to directly …
We study the connection between the phase behaviour of quantum dimers and the dynamics of classical stochastic dimers. At the so-called Rokhsar-Kivelson (RK) point a quantum dimer Hamiltonian is equivalent to the Markov generator of the dynamics of classical dimers. A less well understood fact is that away from the RK point the quantum-classical connection persists: in this case the Hamiltonian corresponds to a non-stochastic "tilted" operator that encodes the statistics of time-integrated observables of the classical stochastic problem. This implies a direct relation between the phase behavio…
In this paper, we study topological properties of 3D lattice dimer model. We demonstrate, that the dimer model on a bipartite lattice possesses topological defects, which are exactly characterized by Hopf invariant. We derive its explicit algebraic expression in terms of effective magnetic field of a dimer configuration. Thus, we solve the problem of topological classification of possible states in 3D lattice dimer model. Furthermore, since the lattice dimer model is known to be dual to spin ice, our work can be viewed as a proposal to search for hopfions in classical, as well as, artificial s…
We discuss phase transitions and the phase diagram of a classical dimer model with anisotropic interactions defined on a square lattice. For the attractive region, the perturbation of the orientational order parameter introduced by the anisotropy causes the Berezinskii-Kosterlitz-Thouless transitions from a dimer-liquid to columnar phases. According to the discussion by Nomura and Okamoto for a quantum-spin chain system [J. Phys. A 27, 5773 (1994)], we proffer criteria to determine transition points and also universal level-splitting conditions. Subsequently, we perform numerical diagonalizati…
We consider dimers on the star lattice (aka the 3-12, Fisher, expanded kagome or triangle-honeycomb lattice). We show that dimer coverings on this lattice have Z_2 arrow and pseudo-spin representations analogous to those for the kagome lattice, and use these to construct an exactly solvable quantum dimer model (QDM) with a Rokhsar-Kivelson (RK) ground state. This QDM, first discussed by Moessner and Sondhi from a different point of view, is the star-lattice analogue of a kagome-lattice QDM analyzed by Misguich et al. We give a detailed analysis of various properties of the classical equal-weig…
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.
I study a dimer model on the square lattice with nearest-neighbor exclusion as the only interaction. Detailed simulations using tomographic entropic sampling show that as the chemical potential is varied, there is a strongly discontinuous phase transition, at which the particle density jumps by about 18% of its maximum value, 1/4. The transition is accompanied by the onset of orientational order, to an arrangement corresponding to the {1/2,0,1/2} structure identified by Phares et al. [Physica B {\bf 409}, 1096 (2011)] in a dimer model with {\it finite} repulsion at {\it fixed} density. Using f…
We consider dynamics of classical dimer models undergoing a phase transition to an ordered, frozen state. Relaxation processes are dominated by traps which are entropic in origin and can be traced to the locally jammed nature of the dimer states. Depending on the nature of the phase transition, critical dynamics are characterized either by an exponential, or sub-exponential in time relaxation of the order parameter. In the latter case relaxation time scales diverge {\em exponentially} as the critical point is approached, following the Vogel-Fulcher law.
In a recent paper [ F. Wang and F. Y. Wu, Phys. Rev. E 75 (2007) 040105(R) ] we reported exact results on the enumeration of close-packed dimers on an infinite kagome lattice. We computed the per-dimer free energy using both the Pfaffian approach and a vertex-model formulation, and found the result given by a simple expression. We also reported results on dimer-dimer correlations without giving details. In this paper we present details of the correlation function analysis. In addition, we extend the exact enumeration to finite lattices under two different boundary conditions and with asymmetri…
We study Heisenberg antiferromagnets on a diamond-like decorated square lattice perturbed by further neighbor couplings. The second-order effective Hamiltonian is calculated and the resultant Hamiltonian is found to be a square-lattice quantum-dimer model with a finite hopping amplitude and no repulsion, which suggests the stabilization of the plaquette phase. Our recipe for constructing quantum-dimer models can be adopted for other lattices and provides a route for the experimental realization of quantum-dimer models.
It is well-known that exact enumerations of close-packed dimers can be carried out for two-dimensional lattices. While details of results are now known for most lattices, due to the unique nature of the lattice structure, there has been no complete analysis for the kagome lattice. Here we derive the close-form expression $(1/3) \ln (4 x y z)$ for the free energy of close-packed dimers on the kagome lattice, where $x,y,z$ are dimer weights. We use two different approaches, the Kasteleyn method of evaluating a Pfaffian and an alternative vertex model formulation. Both methods lead to the same fi…
Random tensor models which display multicritical behaviors in a remarkably simple fashion are presented. They come with entropy exponents γ= (m-1)/m, similarly to multicritical random branched polymers. Moreover, they are interpreted as models of hard dimers on a set of random lattices for the sphere in dimension three and higher. Dimers with their exclusion rules are generated by the different interactions between tensors, whose coupling constants are dimer activities. As an illustration, we describe one multicritical point, which is interpreted as a transition between the dilute phase and a …
Tensor network investigation of the monomer-dimer model on the honeycomb lattice
Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Department of Physics, City University of Hong Kong（香港城市大学物理系）；City University of Hong Kong Shenzhen Research Institute（香港城市大学深圳研究院）
Percolation and jamming phenomena are investigated for anisotropic sequential deposition of dimers (particles occupying two adjacent adsorption sites) on a square lattice. The influence of dimer alignment on the electrical conductivity was examined. The percolation threshold for deposition of dimers was lower than for deposition of monomers. Nevertheless, the problem belongs to the universality class of random percolation. The lowest percolation threshold (pc = 0.562) was observed for isotropic orientation of dimers. It was higher (pc = 0.586) in the case of dimers aligned strictly along one d…
We study hard dimers on dynamical lattices in arbitrary dimensions using a random tensor model. The set of lattices corresponds to triangulations of the d-sphere and is selected by the large N limit. For small enough dimer activities, the critical behavior of the continuum limit is the one of pure random lattices. We find a negative critical activity where the universality class is changed as dimers become critical, in a very similar way hard dimers exhibit a Yang-Lee singularity on planar dynamical graphs. Critical exponents are calculated exactly. An alternative description as a system of `c…
We study a model of two-dimensional classical dimers on the square lattice with strong geometric constraints (there is exactly one bond with the nearest point for every point in the lattice). This model corresponds to the quantum dimer model suggested by D.S. Rokhsar and S.A. Kivelson (1988). We use the directed-loop algorithm to show the system undergoes a Berezinskii-Kostelitz Thousless transition (BKT transition) in finite temperatures. After that, if we destroy the geometric constraint of dimers, the topological transition will transfer to a quasi one-order transition. For the dimer update…
We study the classical hard-core dimer model on the triangular lattice. Following Kasteleyn's fundamental theorem on planar graphs, this problem is soluble by Pfaffians. This model is particularly interesting for, unlike the dimer problems on the bipartite square and hexagonal lattices, its correlations are short ranged with a correlation length of less than one lattice constant. We compute the dimer-dimer and monomer-monomer correlators, and find that the model is deconfining: the monomer-monomer correlator falls off exponentially to a constant value sin(pi/12)/sqrt(3) = .1494..., only slight…
We derive exact results for close-packed dimers on the triangular kagome lattice (TKL), formed by inserting triangles into the triangles of the kagome lattice. Because the TKL is a non-bipartite lattice, dimer-dimer correlations are short-ranged, so that the ground state at the Rokhsar-Kivelson (RK) point of the corresponding quantum dimer model on the same lattice is a short-ranged spin liquid. Using the Pfaffian method, we derive an exact form for the free energy, and we find that the entropy is 1/3 ln2 per site, regardless of the weights of the bonds. The occupation probability of every bon…
We have extended, in most cases through 24th order, the series expansions of the dimer density in powers of the activity in the case of bipartite ((hyper)-simple-cubic and (hyper)-body-centered-cubic) lattices of dimensionalities 2<= d <= 7. A numerical analysis of these data yields estimates of the exponents characterizing the Yang-Lee edge-singularities for lattice ferromagnetic spin-models as d varies between the lower and the upper critical dimensionalities. Our results are consistent with, but more extensive and sometimes more accurate than those obtained from the existing dimer series or…
We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D.S. Rokhsar and S.A. Kivelson, Phys. Rev. Lett.{\bf 61}, 2376 (1988)]. By means of Monte Carlo and Transfer Matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separating a low temperature ordered phase where dimers are aligned in columns from a high temperature critical phase with continuously varying exponents. This is understood by constructing the corresponding …
We consider a classical interacting dimer model which interpolates between the square lattice case and the triangular lattice case by tuning a chemical potential in the diagonal bonds. The interaction energy simply corresponds to the number of plaquettes with parallel dimers. Using transfer matrix calculations, we find in the anisotropic triangular case a succession of different physical phases as the interaction strength is increased: a short range disordered liquid dimer phase at low interactions, then a critical phase similar to the one found for the square lattice, and finally a transition…
We study phases and transitions of the square-lattice double dimer model, consisting of two coupled replicas of the classical dimer model. As on the cubic lattice, we find a thermal phase transition from the Coulomb phase, a disordered but correlated dimer liquid, to a phase where fluctuations of the two replicas are closely synchronized with one another. Surprisingly, and in contrast to the cubic case, the phase boundary includes the noninteracting point, as we establish using a symmetry-based analysis of an effective height theory, indicating that infinitesimal coupling is sufficient to sync…
We solve the monomer-dimer problem on a non-bipartite lattice, the simple quartic lattice with cylindrical boundary conditions, with a single monomer residing on the boundary. Due to the non-bipartite nature of the lattice, the well-known method of a Temperley bijection of solving single-monomer problems cannot be used. In this paper we derive the solution by mapping the problem onto one on close-packed dimers on a related lattice. Finite-size analysis of the solution is carried out. We find from asymptotic expansions of the free energy that the central charge in the logarithmic conformal fiel…
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 3D inverted-XY universality class. By adding aligning interactions…
We reassess the relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers. In the absence of randomness we determine the density and line tension of the polymers in terms of the bond weights of hard-core dimers on the square and the hexagonal lattice. For the latter, we demonstrate the equivalence of the canonical ensemble for the dimer model and the grand-canonical description for polymers by performing explicitly the continuum limit. Using this equivalence for the random bond dimer model on a square lattice, we resolve a previo…
We explicitly show that the Rokhsar-Kivelson dimer model on the triangular lattice is a liquid with topological order. Using the Pfaffian technique, we prove that the difference in local properties between the two topologically degenerate ground states on the cylinders and on the tori decreases exponentially with the system size. We compute the relevant correlation length and show that it equals the correlation length of the vison operator.
Machine learning methods are being actively considered as a new tool of describing many body physics. However, so far, their capabilities has been only demonstrated in previously studied models, such as e.g. Ising model. Here, we consider a simple problem, demonstrating that neural networks can be successfully used to give new insights in statistical physics. Specifically, we consider 3D lattice dimer model, which consists of sites forming a lattice and bonds connecting the neighboring sites, in such a way that every bond can be either empty or filled with a dimer, and the total number of dime…
In a recent paper S. Friedland and the author presented a formal expression for lambda_d(p) of the monomer-dimer problem on a d-dimensional rectangular lattice, which involved a power series in p. Herein, we find simlar expressions for lambda_tri(p) and lambda_hex(p), the entropy per site for triangular and hexagonal lattices.
Quantum dimer models are known to host topological quantum spin liquid phases, and it has recently become possible to simulate such models with Rydberg atoms trapped in arrays of optical tweezers. Here, we present large-scale quantum Monte Carlo simulation results on an extension of the triangular lattice quantum dimer model with terms in the Hamiltonian annihilating and creating single dimers. We find distinct odd and even $\mathbb{Z}_2$ spin liquids, along with several phases with no topological order: a staggered crystal, a nematic phase, and a trivial symmetric phase with no obvious broken…
We report studies of random sequential adsorption on the pre-patterned Bethe lattice. We consider a partially covered Bethe lattice, on which monomers and dimers deposit competitively. Analytical solutions are obtained and discussed in the context of recent efforts to use pre-patterning as a tool to improve self-assembly in micro- and nano-scale surface structure engineering.
We study a generalized quantum hard-core dimer model on the square and honeycomb lattices, allowing for first and second neighbor dimers. At generalized RK points, the exact ground states can be constructed, and ground-state correlation functions can be equated to those of interacting 1+1 dimensional Grassmann fields. When the concentration of second neighbor dimers is small, the ground state correlations are shown to be short-ranged corresponding to a (gaped) spin liquid phase. On a 2-torus, the ground states exhibit fourfold topological degeneracy. On a finite cylinder we have found a dramat…
We investigate the spatially anisotropic square lattice quantum antiferromagnet. The model describes isotropic spin-1/2 Heisenberg chains (exchange constant J) coupled antiferromagnetically in the transverse (J_\perp) and diagonal (J_\times), with respect to the chain, directions. Classically, the model admits two ordered ground states -- with antiferromagnetic and ferromagnetic inter-chain spin correlations -- separated by a first order phase transition at J_\perp=2J_\times. We show that in the quantum model this transition splits into two, revealing an intermediate quantum-disordered columna…
Intractable enumeration problems are like Russian nesting dolls: structural properties of monomer-dimer coverings on two-dimensional quadratic lattices
We consider close-packed dimers, or perfect matchings, on two-dimensional regular lattices. We review known results and derive new expressions for the free energy, entropy, and the molecular freedom of dimers for a number of lattices including the simple-quartic (4^4), honeycomb (6^3), triangular (3^6), kagome (3.6.3.6), 3-12 (3.12^2) and its dual [3.12^2], and 4-8 (4.8^2) and its dual Union Jack [4.8^2] Archimedean tilings. The occurrence and nature of phase transitions are also analyzed and discussed.
We discuss the ground state of the spin-orbital model for spin-one ions with partially filled $t_{2g}$ levels on a honeycomb lattice. We find that the orbital degrees of freedom induce a spontaneous dimerization of spins and drive them into nonmagnetic manifold spanned by hard-core dimer (spin-singlet) coverings of the lattice. The cooperative ``dimer Jahn-Teller'' effect is introduced through a magnetoelastic coupling and is shown to lift the orientational degeneracy of dimers leading to a peculiar valence bond crystal pattern. The present theory provides a theoretical explanation of nonmagne…
We study a large-N deformation of the S=1/2 pyrochlore Heisenberg antiferromagnet which leads to a soluble quantum dimer model at leading non-trivial order. In this limit, the ground state manifold -- while extensively degenerate -- breaks the inversion symmetry of the lattice, which implies a finite temperature Ising transition without translational symmetry breaking. At lower temperatures and further in the 1/N expansion, we discuss an effective Hamiltonian within the degenerate manifold, which has a transparent physical interpretation as representing dimer potential energies. We find mean-f…
