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 gauge-invariant bilinear scalar fields breaking the global SU(N ) symmetry, and to the confinement/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.

Breaking the gauge symmetry in lattice gauge-invariant models.

“…They are expected to correspond to the stable fixed points with nonvanishing gauge couplings (we will name them charged fixed points) that occur in the statistical field theories that are obtained in the formal continuum limit, i.e., that have the same field content and the same global and local symmetries. At present, this type of transitions have been observed in Abelian models-specifically, in the lattice Abelian-Higgs model with noncompact fields [13] or with compact doubly-charged fields [12]-and in an SU(2) gauge model with SU(N f ) global invariance [14].…”

“…Our extensive work on models with Hamiltonian (2) shows [8][9][10][11][12][13][14] that phase transitions occurring in gauge models can be divided into two broad classes. First of all, there are transitions…”

Breaking the gauge symmetry in lattice gauge-invariant models

“…They are expected to correspond to the stable fixed points with nonvanishing gauge couplings (we will name them charged fixed points) that occur in the statistical field theories that are obtained in the formal continuum limit, i.e., that have the same field content and the same global and local symmetries. At present, this type of transitions have been observed in Abelian models-specifically, in the lattice Abelian-Higgs model with noncompact fields [13] or with compact doubly-charged fields [12]-and in an SU(2) gauge model with SU(𝑁 𝑓 ) global invariance [14].…”

“…Our extensive work on models with Hamiltonian (2) shows [8][9][10][11][12][13][14] that phase transitions occurring in gauge models can be divided into two broad classes. First of all, there are transitions where only scalar-matter correlations are critical.…”

Non-compact lattice Higgs model with Abelian discrete gauge groups: phase diagram and gauge symmetry enlargement

“…Examples of this behavior are found in the multicomponent non-compact lattice Abelian Higgs model [28][29][30] , in the multicomponent compact lattice Abelian Higgs model with charge Q ≥ 2 (see Refs. 31,32 ), and also in some non-Abelian models 23,34,35 .…”