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arXiv:2204.11260

Evolution of phase transition in the finite-fugacity extended dimer model

Yao Hongxu, Jiaze Li, Hou Jintao, Jie Lou, Yan Chen

Published Apr 24, 2022• 0 citations
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Abstract

We investigate the evolution of phase transition of the classical fully compact dimer model on the bipartite square lattice with second nearest bonds at finite temperatures. We use the numeric Monte Carlo method with the directed-loop algorithm to simulate the model. Our results show that the order of the phase transition depends on the fugacity of the second nearest bonds. We find that the phase transition reduces from the Kosterlitz-Thouless transition to unconventional high-order phase transitions which feature the coexistence of properties Kosterliz-Thouless transition and the first-order phases transition simultaneously. As the fugacity increases further, phase transition evolves to the first-order phase transition. In addition, our results of dimer-dimer correlation functions and their corresponding structure factor functions computed by us show the evolution of decay correlation for different fugacity.

DOI
10.48550/arxiv.2204.11260

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We investigate the evolution of phase transition of the classical fully compact dimer model on the bipartite square lattice with second nearest bonds at finite temperatures. We use the numeric Monte Carlo method with the directed-loop algorithm to simulate the model. Our results show that the order of the phase transition depends on the fugacity of the second nearest bonds. We find that the phase transition reduces from the Kosterlitz-Thouless transition to unconventional high-order phase transitions which feature the coexistence of properties Kosterliz-Thouless transition and the first-order phases transition simultaneously. As the fugacity increases further, phase transition evolves to the first-order phase transition. In addition, our results of dimer-dimer correlation functions and their corresponding structure factor functions computed by us show the evolution of decay correlation for different fugacity.
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. 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 Coulomb gas, whose coupling constant is computed numerically. We also discuss doped models and implications on the finite-temperature phase diagram of quantum dimer models.
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 mapping the model to a Coulomb gas, whose coupling constant and associated exponents are calculated numerically with high precision. Introducing monomers is a marginal perturbation at the Kosterlitz-Thouless transition and gives rise to another critical line. We study this line numerically, showing that it is in the Ashkin-Teller universality class, and terminates in a tricritical point at finite temperature and monomer fugacity. In the course of this work, we also derive analytic results relevant to the noninteracting case of dimer coverings, including a Bethe ansatz (at the free fermion point) analysis, a detailed discussion of the effective height model, and a free field analysis of height fluctuations.
We use Monte Carlo simulations and tensor network methods to study a classical monomer-dimer model on the square lattice with a hole (monomer) fugacity zzz, an aligning dimer-dimer interaction uuu that favors columnar order, and an attractive dimer-dimer interaction vvv between two adjacent dimers that lie on the same principal axis of the lattice. The Monte Carlo simulations of finite size systems rely on our grand-canonical generalization of the dimer worm algorithm, while the tensor network computations are based on a uniform matrix product ansatz for the eigenvector of the row-to-row transfer matrix that work directly in the thermodynamic limit. The phase diagram has nematic, columnar order and fluid phases, and a nonzero temperature multicritical point at which all three meet. For any fixed $v/u<\ensuremath{\infty}$, we argue that this multicritical point continues to be located at a nonzero hole fugacity zmc(v/u)>0{z}_{\mathrm{mc}}(v/u)>0zmc​(v/u)>0; our numerical results confirm this theoretical expectation but find that ${z}_{\mathrm{mc}}(v/u)\ensuremath{\rightarrow}0$ very rapidly as $v/u\ensuremath{\rightarrow}\ensuremath{\infty}$. Our numerical results also confirm the theoretical expectation that the corresponding multicritical behavior is in the universality class of the four-state Potts multicritical point on critical line of the two-dimensional Ashkin-Teller model.
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∕r21∕{r}^{2}1∕r2, although the logarithmic peaks present in the dimer structure factor of the nearest-neighbor model vanish. By contrast, an arbitrarily small fraction of next-nearest-neighbor dimers leads to the onset of exponential dimer correlations and deconfinement. We discuss these results in the framework of effective theories, and provide an approximate but accurate analytical expression for the dimer correlations.
Using the tensor network approach, we investigate the monomer-dimer models on a checkerboard lattice, in which there are interactions (with strength vvv) 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 low-temperature symmetry breaking and the high-temperature critical phases; for the doped monomer-dimer case with finite chemical potential $\ensuremath{\mu}$, we also find an order-disorder phase transition which is of second order instead. We use the boundary matrix product state approach to detect the KT and second-order phase transitions and obtain the phase diagrams $v\text{\ensuremath{-}}T$ and $\ensuremath{\mu}\text{\ensuremath{-}}T$. Moreover, for the noninteracting monomer-dimer model (setting $\ensuremath{\mu}=\ensuremath{\nu}=0$), we get an extraordinarily accurate determination of the free energy per site (negative of the monomer-dimer constant h2{h}_{2}h2​) as $f=\ensuremath{-}0.662\phantom{\rule{0.16em}{0ex}}798\phantom{\rule{0.16em}{0ex}}972\phantom{\rule{0.16em}{0ex}}833\phantom{\rule{0.16em}{0ex}}746$ with the dimer density n=0.638123109228547n=0.638\phantom{\rule{0.16em}{0ex}}123\phantom{\rule{0.16em}{0ex}}109\phantom{\rule{0.16em}{0ex}}228\phantom{\rule{0.16em}{0ex}}547n=0.638123109228547, both of 15 correct digits.
By means of quantum Monte Carlo simulations implemented with a two-loop update scheme, the finite-temperature phase diagram of a three-body constrained attractive Bose lattice gas is investigated. The nature of the thermal phase transitions around the dimer superfluid and the atomic superfluid is unveiled. We find that the Z2{Z}_{2}Z2​ symmetry breaking transitions between these two superfluid phases are of first order even at nonzero temperatures. More interestingly, the thermal transition from the dimer superfluid to the normal fluid is found to be consistent with the Kosterlitz-Thouless type but giving an anomalous universal stiffness jump. It demonstrates that this transition is driven by unbinding of pairs of fractional vortices.