Higher-charge three-dimensional compact lattice Abelian-Higgs models

Abstract

We consider three-dimensional higher-charge multicomponent lattice Abelian-Higgs (AH) models, in which a compact U(1) gauge field is coupled to an N-component complex scalar field with integer charge q, so that they have local U(1) and global SU(N) symmetries. We discuss the dependence of the phase diagram, and the nature of the phase transitions, on the charge q of the scalar field and the number N 2 of components. We argue that the phase diagram of higher-charge models presents three different phases, related to the condensation of gaugeinvariant bilinear scalar fields breaking the global SU(N) symmetry, and to the confinement and deconfinement of external charge-one particles. The transition lines separating the different phases show different features, which also depend on the number N of components. Therefore, the phase diagram of higher-charge models substantially differs from that of unit-charge models, which undergo only transitions driven by the breaking of the global SU(N) symmetry, while the gauge correlations do not play any relevant role. We support the conjectured scenario with numerical results, based on finite-size scaling analyses of Monte Carlo simuations for doubly charged unit-length scalar fields with small and large number of components, i.e., N = 2 and N = 25.

Critical behaviors of lattice U(1) gauge models and three-dimensional Abelian-Higgs gauge field theory

“…Therefore, one would expect that the field-theory CFP of the RG flow of the AH field theory is the one that controls the universal features of the critical transitions of type (ii) in AH lattice models. Critical behaviors consistent with the universality classes of the AH field theory have been observed in the lattice AH model with noncompact gauge fields [38] (along the transition line that separates the Coulomb and the Higgs phase), and in the lattice AH model with compact gauge fields and q = 2 scalar charge [39] (along the transition line between the confined and the deconfined phase). We also mention that continuous transitions of type (ii) have been observed in a different lattice U(1) gauge model, in the CP N −1 model without monopoles [21].…”

“…[38] obtained ν = 0.802 (8) for the compact model with q = 2, while Ref. [39] reported ν = 0.815 (15) for the noncompact model. As for η q , previous estimates The continuous line is an extrapolation of the data for the noncompact model [38]; noncompact-model data for L = 48 and L = 64 are also reported to provide an estimate of the accuracy of the extrapolation.…”

“…We have considered two values of q, q = 2 and 3, and, for each of them, we have performed simulations at a fixed value of κ, chosen so that the transition belongs to the DC-OD line. For q = 2, simulations were already performed [39] fixing κ = 1 and using periodic boundary conditions, identifying the transition at J c = 0.29333 (3). For q = 3, the results of Ref.…”

“…For q ≥ 2 the phase diagram is more complex, see Fig. 1 (bottom), with three different phases [39,[62][63][64][65][66][67][68]. They are characterized by the large-distance behavior of both scalar and gauge observables.…”

“…It has been realized that a crucial role is played by topological aspects, like Berry phases, monopoles, or the compact/noncompact nature of the U(1) gauge fields, together with the charge of the scalar fields. Indeed, the phase diagram and the nature of the transitions is different in lattice AH models with compact and noncompact gauge fields [18,38], in AH compact models with charge-one and higher-charge scalar fields [18,39], and in models with or without topological defects such as monopoles [19][20][21]40].…”