The critical behavior of a dimer model with an interaction favoring parallel dimers in each plaquette of the square lattice is studied numerically by means of the Corner Transfer Matrix Renormalization Group algorithm. The critical exponents are known to depend on the chemical potential of vacancies, or monomers. At large average density of the latter, the phase transition becomes of first-order. We compute the scaling dimensions of both order parameter and temperature in the second order regime and compare them with the conjecture that the critical behavior is the same as the Ashkin-Teller model on its self-dual critical line.
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…
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…
We study a modified version of the interacting monomer-dimer (IMD) model that has infinitely many absorbing (IMA) states. Unlike all other previously studied models with IMA states, the absorbing states can be divided into two equivalent groups which are dynamically separated infinitely far apart. Monte Carlo simulations show that this model belongs to the directed Ising universality class like the ordinary IMD model with two equivalent absorbing states. This model is the first model with IMA states which does not belong to the directed percolation (DP) universality class. The DP universality …
The thermodynamic properties of two-component Fermi gases with divergent scattering length is investigated and the transition temperature for the emergence of a stable dimeric gas is obtained by a simple theoretical model where the unique property of the dimers (i.e. fermionic atom pairs) with divergent scattering length is considered. Below the transition temperature, through the investigation of the overall entropy for the mixture gas of fermionic atoms and dimers, we calculate the relation between the energy and temperature of the system. In the limit of zero temperature, based on the chemi…
We study the order-disorder transition of the two dimensional interacting monomer-dimer model (IMD) which has two symmetric absorbing states. To be self-contained, we first estimate numerically the dynamic exponent $z$ of the two dimensional Ising model. From the relaxation dynamics of the magnetization at the critical point, we obtain $β/(νz) = 0.057~650(12)$, or $z = 2.168 26(45)$, where $β= \frac{1}{8}$ and $ν=1$ are exactly known exponents. We, then, compare the critical relaxation of the order parameter at the transition point of the IMD with that of the Ising model. We found that the cri…
We consider a monomer-dimer system with a strong attractive dimer-dimer interaction that favors alignment. In 1979, Heilmann and Lieb conjectured that this model should exhibit a nematic liquid crystal phase, in which the dimers are mostly aligned, but do not manifest any translational order. We prove this conjecture for large dimer activity and strong interactions. The proof follows a Pirogov-Sinai scheme, in which we map the dimer model to a system of hard-core polymers whose partition function is computed using a convergent cluster expansion.
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 show the emergence of a strongly interacting Bose-Fermi mixture from a two-component Fermi mixture with population imbalance. By analyzing in situ density profiles of $^6$Li atoms in the BCS-BEC crossover regime we identify a critical interaction strength, beyond which all minority atoms pair up with majority atoms, and form a Bose condensate. This is the regime where the system can be effectively described as a boson-fermion mixture. We determine the dimer-fermion and dimer-dimer scattering lengths and beyond-mean-field contributions. Our study realizes a Gedanken experiment of bosons imme…
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 consider a model of weakly interacting, close-packed, dimers on the two-dimensional square lattice. In a previous paper, we computed both the multipoint dimer correlations, which display non-trivial critical exponents, continuously varying with the interaction strength; and the height fluctuations, which, after proper coarse graining and rescaling, converge to the massless Gaussian field with a suitable interaction-dependent pre-factor (`amplitude'). In this paper, we prove the identity between the critical exponent of the two-point dimer correlation and the amplitude of this massless Gauss…
We uncover a novel mechanism for inducing a gapful phase in interacting many-body quantum chains. The mechanism is nonperturbative, being triggered only in the presence of both strong interactions and strong aperiodic (disordered) modulation. In the context of the critical antiferromagnetic spin-1/2 XXZ chain, we identify an emerging dimerization which removes the system from criticality and stabilizes the novel phase. This mechanism is shown to be quite general in strongly interacting quantum chains in the presence of strongly modulated quasiperiodic disorder which is, surprisingly, perturbat…
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…
We study the phase transition in a system composed of dimers interacting with each other via a nearest-neighbor (NN) exchange $J$ and competing interactions taken from a truncated dipolar coupling. Each dimer occupies a link between two nearest sites of a simple cubic lattice. We suppose that dimers are self-avoiding and can have only three orientations which coincide with the $x$, $y$ or $z$ direction. The interaction $J$ is attractive if the two dimers are parallel with each other at the NN distance, zero otherwise. The truncated dipolar interaction is characterized by two parameters: its am…
In the last few years, the methods of constructive Fermionic Renormalization Group have been successfully applied to the study of the scaling limit of several two-dimensional statistical mechanics models at the critical point, including: weakly non-integrable 2D Ising models, Ashkin-Teller, 8-Vertex, and close-packed interacting dimer models. In this note, we will focus on the illustrative example of the interacting dimer model and review some of the universality results derived in this context. In particular, we will discuss the massless Gaussian free field (GFF) behavior of the height fluctu…
We study a system of interacting triplons (the elementary excitations of a valence-bond solid) described by an effective interacting boson model derived within the bond-operator formalism. In particular, we consider the square lattice spin-1/2 $J_1$-$J_2$ antiferromagnetic Heisenberg model, focus on the intermediate parameter region, where a quantum paramagnetic phase sets in, and consider the columnar valence-bond solid phase. Within the bond-operator theory, the Heisenberg model is mapped into an effective boson model in terms of triplet operators $t$. The effective boson model is studied at…
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 present a quantum Monte Carlo investigation of the finite-temperature phase diagram of the quantum dimer model on the square lattice. We use the sweeping cluster algorithm, which allows to implement exactly the dimer constraint, supplemented with a equal-time directed loop move that allows to sample winding sectors. We find a high-temperature critical phase with power-law correlations that extend down to the Rokshar-Kivelson point, in the vicinity of which a re-entrance effect in the lines of constant exponent is found. For small values of the kinetic energy strength, we find finite-tempera…
The critical point of the condensation transition for linear molecules adsorbed on square lattices, was studied by using an adaptation of the Histogram Reweighting technique. The results were obtained by means of grand canonical Monte Carlo simulations within the lattice gas model, along with finite size scaling using the fourth order Binder cumulant. The Method was tested in a system of interacting monomers in which the critical point can be determined exactly. The application of this method to the determination of the critical point in dimer systems with attractive interactions, gave better …
We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase. With large-scale Monte Carlo and Transfer Matrix calculations, we show that the crystal melts through a Kosterlitz-Thouless phase transition to give rise to a high-temperature critical phase, with algebraic decays of correlations functions with exponents that vary continuously with the temperature. We give a theoretical interpretation of these results by map…
A Monte Carlo computer simulation algorithm in classical phase space is given for the treatment of quantum systems. The non-commutativity of position and momentum is accounted for by a mean field approach and instantaneous effective harmonic oscillators. Wave function symmetrization is included at the dimer and double dimer level. Quantitative tests are performed against benchmarks given by Hernando and Vaníček (2013) for spinless neon--parahydrogen, modeled as interacting Lennard-Jones particles in a one dimensional harmonic trap. The mean field approach is shown to be quantitatively accurate…
We construct a local interacting quantum dimer model on the square lattice, whose zero-temperature phase diagram is characterized by a line of critical points separating two ordered phases of the valence bond crystal type. On one side, the line of critical points terminates in a quantum transition inherited from a Kosterlitz-Thouless transition in an associated classical model. We also discuss the effect of a longer-range dimer interactions that can be used to suppress the line of critical points by gradually shrinking it to a single point. Finally, we propose a way to generalize the quantum H…
We examine the scaling behavior of the entanglement entropy for the 2D quantum dimer model (QDM) at criticality and derive the universal finite sub-leading correction $γ_{QCP}$. We compute the value of $γ_{QCP}$ without approximation working directly with the wave function of a generalized 2D QDM at the Rokhsar-Kivelson QCP in the continuum limit. Using the replica approach, we construct the conformal boundary state corresponding to the cyclic identification of $n$-copies along the boundary of the observed region. We find that the universal finite term is $γ_{QCP}=\ln R-1/2$ where $R$ is the c…
