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arXiv:1104.0467 · Physical Review Letters

Monomer-Dimer Mixture on a Honeycomb Lattice

Hiromi Otsuka

Published Jun 3, 2011• 8 citations
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Abstract

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 M5 and M6 in the minimal models of the conformal field theory. We perform numerical transfer-matrix calculations to determine a global phase diagram and also to proffer evidence to check our prediction.

DOI
10.1103/physrevlett.106.227204

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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 M5 and M6 in the minimal models of the conformal field theory. We perform numerical transfer-matrix calculations to determine a global phase diagram and also to proffer evidence to check our prediction.
We study a monomer-dimer mixture on a honeycomb lattice as a simplified model for a spin ice in two dimension. In a low monomer-density region, an effective description is given by the dual sine-Gordon theory. On the other hand, in intermediate and high monomer-density regions, the Potts lattice-gas theory can be adopted. Based on these, we extract a renormalization-group flow diagram, which includes stable and unstable fixed points corresponding to M 5 and M 6 in the minimal models of the conformal field theory. We carry out numerical transfer-matrix calculations to determine the phase diagram, and we provide evidence to check our prediction.
The spin-1/21/21/2 quantum Heisenberg model on the diamond-decorated honeycomb lattice in a magnetic field is investigated using complementary analytical and numerical methods. The ground-state phase diagram comprises Lieb-Mattis ferrimagnetic, dimer-tetramer, monomer-dimer, spin-canted, and saturated paramagnetic phases, giving rise to characteristic magnetization plateaus, continuous and discontinuous field-induced transitions. In the highly frustrated regime, a localized-magnon approach based on an effective classical lattice-gas model provides an accurate description of the low-temperature magnetism and thermodynamics in agreement with numerical results. At intermediate frustration, finite-temperature calculations reveal characteristic specific-heat signatures of the field-induced transitions including the development of Ising critical behavior at the field-induced transition between the monomer-dimer and Lieb-Mattis ferrimagnetic phase.
Abstract We investigate the spin-1/2 Heisenberg antiferromagnet on a distorted diamond-decorated honeycomb lattice in an external magnetic field. By combining density-matrix renormalization group, sign-problem-free quantum Monte Carlo in a mixed dimer–monomer basis, exact diagonalization, and an effective lattice-gas approach, we determine the ground-state phase diagram and analyze the finite-temperature magnetization process. The model hosts a rich variety of frustration-induced quantum phases including a quantum ferrimagnetic phase of Lieb–Mattis type, a quantum ferromagnetic phase, a spin-canted phase, a monomer–dimer phase, a dimer–tetramer liquid, a dimer-tetramer solid, and two distinct one-dimensional-crossover phases of ferromagnetic and ferrimagnetic character. Depending on the lattice distortion, we identify robust magnetization plateaus at 0, 1/4, 1/2, and 3/4 of the saturation magnetization originating from competing local dimer and tetramer singlets. Finite-temperature QMC data reveal how thermal fluctuations progressively smear the plateau structure, while the effective lattice-gas description reliably captures the corresponding low-temperature behavior.
The spin-1/2 Heisenberg antiferromagnet on the diamond-decorated square lattice in the presence of a magnetic field displays various quantum phases including the Lieb-Mattis ferrimagnetic, dimer-tetramer, monomer-dimer, and spin-canted phases, in addition to the trivial fully saturated state. Thermodynamic properties of this model are investigated using several complementary analytical and numerical methods such as exact diagonalization up to the systems of 40 spins, an effective monomer-dimer description, sign-problem-free quantum Monte Carlo simulations for up to 180 spins, and a decoupling approximation. Our particular attention is focused on the parameter region favoring the dimer-tetramer phase. This ground state can be represented by a classical hard-dimer model on the square lattice and retains a macroscopic degeneracy even under a magnetic field. However, the description of the low-temperature thermodynamics close to the boundary between the macroscopically degenerate dimer-tetramer and the nondegenerate monomer-dimer phases requires an extended classical monomer-dimer lattice-gas model. Anomalous thermodynamic properties emerging in the vicinity of the dimer-tetramer phase are studied in detail. Under the adiabatic demagnetization we detect an enhanced magnetocaloric effect promoting an efficient cooling to absolute zero temperature.
A two-dimensional lattice-gas model with honeycomb symmetry is investigated by using the real-space renormalization group (RSRG) approach with a number of RSRG transformations based on clusters of different symmetries and sizes (up to 42 sites). The accuracy of calculations is found to be a nonmonotonic function of the size of a cluster, and to depend strongly on its symmetry. The highest obtained accuracy with respect to the determination of the critical value of the pair interaction parameter is 0.38%. The phase diagram of the Ising antiferromagnetic spin model and of the corresponding lattice-gas model is constructed with this accuracy. The ordered phase in the lattice system is shown to appear in the very narrow density interval, 0.447<n<0.553.0.447<n<0.553.0.447<n<0.553. In addition, the coverage dependence of the chemical diffusion coefficient and mean-square density fluctuations are studied at temperatures below the critical one. Both quantities are demonstrated to exhibit singularities at the critical coverages. The type of singularities (in particular, the critical slowdown of diffusion) is in agreement with the predictions of the scaling theory and also with recent results obtained for a model treating the effect of surface reconstruction on diffusion.
The monomer-dimer model is one of the most well-known unsolved lattice models. In this paper we study the monomer-dimer model on the honeycomb lattice using the tensor network method, in the case that the dimer and monomer activities are 1. The monomer-dimer configurations are exactly mapped into the ground states of the antiferromagnetic Ising model on the Kagomé lattice in the critical field Hex=4JH_{\rm{ex}}=4JHex​=4J, and the tensor network is constructed based on the local ground states of each Ising triangle. The VUMPS approach is employed to contract the tensor network, providing a high-precision result of the monomer-dimer problem. We also revisit the edge coloring problem on the honeycomb lattice and discuss its relationship to the monomer-dimer model. Finally we formulate the monomer-dimer problem in the language of the sixteen-vertex model, and discuss the non-integrability of the general monomer-dimer model and the integrability of the pure dimer model.