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arXiv:1504.02278 · Physical Review B

Scaling dimensions of higher-charge monopoles at deconfined critical points

G. J. Sreejith, Stephen Powell

Published Nov 17, 2015• 40 citations
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Abstract

The classical cubic dimer model has a columnar ordering transition that is continuous and described by a critical Anderson-Higgs theory containing an $\mathrm{SU}(2)$-symmetric complex field minimally coupled to a noncompact $\mathrm{U}(1)$ gauge theory. Defects in the dimer constraints correspond to monopoles of the gauge theory, with charge determined by the deviation from unity of the dimer occupancy. By introducing such defects into Monte Carlo simulations of the dimer model at its critical point, we determine the scaling dimensions ${y}_{2}=1.48\ifmmode\pm\else\textpm\fi{}0.07$ and ${y}_{3}=0.20\ifmmode\pm\else\textpm\fi{}0.03$ for the operators corresponding to defects of charge $q=2$ and 3, respectively. These results, which constitute the first direct determination of the scaling dimensions, shed light on the deconfined critical point of spin-$\frac{1}{2}$ quantum antiferromagnets, thought to belong to the same universality class. In particular, the positive value of ${y}_{3}$ implies that the transition in the $JQ$ model on the honeycomb lattice is of first order.

DOI
10.1103/physrevb.92.184413

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The classical cubic dimer model has a columnar ordering transition that is continuous and described by a critical Anderson-Higgs theory containing an SU(2)\mathrm{SU}(2)SU(2)-symmetric complex field minimally coupled to a noncompact U(1)\mathrm{U}(1)U(1) gauge theory. Defects in the dimer constraints correspond to monopoles of the gauge theory, with charge determined by the deviation from unity of the dimer occupancy. By introducing such defects into Monte Carlo simulations of the dimer model at its critical point, we determine the scaling dimensions y2=1.48\ifmmode±\else\textpm\fi0.07{y}_{2}=1.48\ifmmode\pm\else\textpm\fi{}0.07y2​=1.48\ifmmode±\else\textpm\fi0.07 and y3=0.20\ifmmode±\else\textpm\fi0.03{y}_{3}=0.20\ifmmode\pm\else\textpm\fi{}0.03y3​=0.20\ifmmode±\else\textpm\fi0.03 for the operators corresponding to defects of charge q=2q=2q=2 and 3, respectively. These results, which constitute the first direct determination of the scaling dimensions, shed light on the deconfined critical point of spin-12\frac{1}{2}21​ quantum antiferromagnets, thought to belong to the same universality class. In particular, the positive value of y3{y}_{3}y3​ implies that the transition in the JQJQJQ model on the honeycomb lattice is of first order.
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 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.
Quantum phase transition from the N\'eel to the dimer states in an antiferromagnetic (AF) Heisenberg model on square lattice is studied. We introduce a control parameter $\ensuremath{\alpha}$ for the exchange coupling that connects the N\'eel $(\ensuremath{\alpha}=0)$ and the dimer $(\ensuremath{\alpha}=1)$ states. We employ the CP1{\mathit{CP}}^{1}CP1 representation of the s=12s=\frac{1}{2}s=21​ spin operator and integrate out the half of the CP1{\mathit{CP}}^{1}CP1 variables at odd sites to obtain a CP1{\mathit{CP}}^{1}CP1 nonlinear $\ensuremath{\sigma}$ model. The effective coupling constant is a function of $\ensuremath{\alpha}$, and at $\ensuremath{\alpha}=0$, the CP1{\mathit{CP}}^{1}CP1 model is in the ordered phase that corresponds to the N\'eel state of the AF Heisenberg model. A phase transition to the dimer state occurs at a certain critical value of ${\ensuremath{\alpha}}_{C}$ as $\ensuremath{\alpha}$ increases. In the N\'eel state, the dynamical composite U(1) gauge field in the CP1{\mathit{CP}}^{1}CP1 model is in a Higgs phase, and low-energy excitations are gapless spin waves. In the dimer phase, a confinement phase of the gauge theory with s=1s=1s=1 excitations is realized. For the critical point, we argue that a deconfinement phase, which is similar to the Coulomb phase in three spatial dimensions, is realized and s=12s=\frac{1}{2}s=21​ spinons appear as low-energy excitations.
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.
Two-dimensional Rokhsar-Kivelson (RK) dimer models on bipartite lattices are generally limited to translation-symmetry-broken dimer crystals. We introduce a tensor-product regularization of the dimer Hilbert space that yields a qubit Hamiltonian interpolating from the RK model to the π -flux toric code, thereby accessing a deconfined Z 2 topological liquid. In this framework, the Z 2 liquid descends from a multicritical U ( 1 ) spin liquid through condensation of a charge-2 Higgs field, thus avoiding confinement. Using iDMRG together with low-energy field theory, we determine a phase diagram containing two continuous quantum phase transitions—a 3 D XY * transition between the Z 2 liquid and the columnar/plaquette-VBS, and a quantum Lifshitz transition between two dimer crystals—alongside a first-order transition between the staggered crystal and the Z 2 liquid. Our field theory suggests a deconfined multicritical point described by an Abelian Higgs model with dynamical critical exponent, z = 2 , where the three transitions meet, highlighting the interplay of fractionalization and emergent gauge fluctuations.
We resolve the nature of the quantum phase transition between antiferromagnetic and valence-bond solid ground states in square-lattice spin-1/2 magnets - the putative deconfined quantum-critical point. Using quantum Monte Carlo simulations of J-Q models, in which Heisenberg exchange J competes with multi-spin interactions Qn formed by n singlet projectors, we demonstrate first-order discontinuities increasing with n. For n=2 and n=3, the first-order signatures are very weak and we extract universal scaling dimensions of a proximate multicritical point. Their values coincide closely with known bounds for an SO(5) symmetric conformal field theory (CFT) containing a relevant SO(5) singlet operator that destabilizes the generic deconfined critical point. We characterize the emergent SO(5) symmetry by its scaling dimensions of the leading irrelevant perturbations. Using the J-Q2-Q6 model, we tune the transition from weak to stronger first-order and find scaling of the coexisting order parameters with a large exponent beta ~ 0.85, in agreement with the relevant scaling dimensions of the multicritical point. The exponent that had previously been identified with the correlation length does not have a corresponding CFT level, and we explain it as pseudo-critical length scale of bubbles of one phase inside the other that are compressed in size by an SO(5)-violating irrelevant repulsive interaction between the two order parameters. The bubble scale reflects a hierarchy of excitation gaps generated by the SO(5) perturbation in the neighborhood of the first-order transition, akin to a Higgs mechanism. We argue that the multicritical point is the tip of a gapless spin liquid phase in frustrated Heisenberg models into which the J-Q models can be deformed, but the spin liquid, and perhaps the multicritical point itself, exist outside the regime amenable to sign-free simulations.