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arXiv:cond-mat/0603499 · Physical Review Letters

Unconventional Continuous Phase Transition in a Three-Dimensional Dimer Model

Fabien Alet, Grégoire Misguich, Vincent Pasquier, Roderich Moessner, Jesper Lykke Jacobsen

Published Jul 21, 2006• 59 citations
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Abstract

Phase transitions occupy a central role in physics, due both to their experimental ubiquity and their fundamental conceptual importance. The explanation of universality at phase transitions was the great success of the theory formulated by Ginzburg and Landau, and extended through the renormalization group by Wilson. However, recent theoretical suggestions have challenged this point of view in certain situations. In this Letter we report the first large-scale simulations of a three-dimensional model proposed to be a candidate for requiring a description beyond the Landau-Ginzburg-Wilson framework: we study the phase transition from the dimer crystal to the Coulomb phase in the cubic dimer model. Our numerical results strongly indicate that the transition is continuous and is compatible with a tricritical universality class, at variance with previous proposals.

DOI
10.1103/physrevlett.97.030403

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Phase transitions occupy a central role in physics, due both to their experimental ubiquity and their fundamental conceptual importance. The explanation of universality at phase transitions was the great success of the theory formulated by Ginzburg and Landau, and extended through the renormalization group by Wilson. However, recent theoretical suggestions have challenged this point of view in certain situations. In this Letter we report the first large-scale simulations of a three-dimensional model proposed to be a candidate for requiring a description beyond the Landau-Ginzburg-Wilson framework: we study the phase transition from the dimer crystal to the Coulomb phase in the cubic dimer model. Our numerical results strongly indicate that the transition is continuous and is compatible with a tricritical universality class, at variance with previous proposals.
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.
Abstract The classical dimer model on the cubic lattice hosts a columnar ordered phase and a disordered Coulomb phase, separated by a continuous phase transition that lies beyond the conventional Landau–Ginzburg–Wilson (LGW) paradigm. While its equilibrium critical properties have been extensively studied, the nonequilibrium critical dynamics of this model—particularly in the short-time regime—remains largely unexplored. In this work, we investigate the short-time critical dynamics near the transition using large-scale Monte Carlo simulations. By quenching the system from both ordered and disordered initial states with vanishing initial correlation length, we analyze the scaling behaviors of the order parameter and its time correlation function in the short-time stage. From these scaling behaviors, we accurately determine the critical temperature T c = 0.672(1) and the static critical exponent β / ν = 0.581(5) according to the scaling theory of the short-time dynamics. These results are in excellent agreement with previous equilibrium studies. Moreover, we extract the dynamic critical exponent z = 1.92(1) and, notably, find a negative critical initial slip exponent θ = − 1.052(5). This unusual negative value contrasts sharply with the positive θ typically observed in conventional critical dynamics. We attribute this anomalous behavior to the combined effects of the emergent SO(5) symmetry at criticality and the local U(1) gauge constraint (Gauss law), which enforces a conserved diffusive dynamics and enhances fluctuations in the short-time regime. Our results provide the first comprehensive characterization of nonequilibrium short-time criticality in the three-dimensional dimer model, shedding new light on the universal dynamical features of phase transitions beyond the LGW framework.
We study critical behavior in the classical cubic dimer model (CDM) in the presence of a finite density of monomers. With attractive interactions between parallel dimers, the monomer-free CDM exhibits an unconventional transition from a Coulomb phase to a dimer crystal. Monomers act as charges (or monopoles) in the Coulomb phase and, at nonzero density, lead to a standard Landau-type transition. We use large-scale Monte Carlo simulations to study the system in the neighborhood of the critical point, and find results in agreement with detailed predictions of scaling theory. Going beyond previous studies of the transition in the absence of monomers, we explicitly confirm the distinction between conventional and unconventional criticality, and quantitatively demonstrate the crossover between the two. Our results also provide additional evidence for the theoretical claim that the transition in the CDM belongs in the same universality class as the deconfined quantum critical point in the SU(2)\mathrm{SU}(2)SU(2) JQ model.
The tricritical Ising universality class emerges at the end point of a line of continuous Ising phase transitions, above which the transition is first order. In 1+1 dimensions, it is described by the second minimal model of conformal field theory (CFT) with central charge c=7/10c=7/10c=7/10. Recently, there has been a revival of interest in the tricritical Ising model due to its emergent space-time supersymmetry. Combining numerical (infinite density-matrix renormalization group) and field theoretical (bosonization and CFT) techniques, there authors demonstrate here that Ising tricriticality occurs in a paradigmatic extended one dimensional Hubbard model with explicit bond dimerization. The low-energy sector can be described by a triple sine-Gordon model, which, in the transition region, reduces to the tricritical Ising CFT. The theoretically predicted decay of various two-point correlation functions is found to be in excellent agreement with the density-matrix renormalization group data.
The classical cubic-lattice dimer model undergoes an unconventional transition between a columnar crystal and a dimer liquid, in the same universality class as the deconfined quantum critical point in spin-1/2 antiferromagnets but with very different microscopic physics and microscopic symmetries. Using Monte Carlo simulations, we show that this transition has emergent SO(5) symmetry relating quantities characterizing the two phases. While the low-temperature phase has a conventional order parameter, the defining property of the Coulomb liquid on the high-temperature side is deconfinement of monomers, and so SO(5) relates fundamentally different types of objects. Studying linear system sizes up to L=96, we find that this symmetry applies with an excellent precision, consistently improving with system size over this range. It is remarkable that SO(5) emerges in a system as basic as the cubic dimer model, with only simple discrete degrees of freedom. Our results are important evidence for the generality of the SO(5) symmetry that has been proposed for the noncompact CP^{1} field theory. We describe an interpretation for these results in terms of a consistent hypothesis for the renormalization-group flow structure, allowing for the possibility that SO(5) may ultimately be a near-symmetry rather than exact.
We present an unbiased numerical density-matrix renormalization group study of the one-dimensional Bose-Hubbard model supplemented by nearest-neighbor Coulomb interaction and bond dimerization. It places the emphasis on the determination of the ground-state phase diagram and shows that, besides dimerized Mott and density-wave insulating phases, an intermediate symmetry-protected topological Haldane insulator emerges at weak Coulomb interactions for filling factor one, which disappears, however, when the dimerization becomes too large. Analyzing the critical behavior of the model, we prove that the phase boundaries of the Haldane phase to Mott insulator and density-wave states belong to the Gaussian and Ising universality classes with central charges c=1c=1c=1 and c=1/2c=1/2c=1/2, respectively, and merge in a tricritical point. Interestingly we can demonstrate a direct Ising quantum phase transition between the dimerized Mott and density-wave phases above the tricritical point. The corresponding transition line terminates at a critical end point that belongs to the universality class of the dilute Ising model with c=7/10c=7/10c=7/10. At even stronger Coulomb interactions the transition becomes first order.