Finite-size scaling analyses of Monte Carlo data for 3D compact lattice U(1) models with doubly-charged N-component scalars show continuous DC-OD transitions for N=10, weak first-order for N≤7, and inconclusive results for N=8,9, yielding the estimate N_cL=9(1).
Comparative study of Higgs transition in one-component and two-component lattice superconductor models
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abstract
Using Monte Carlo simulations, we study a Higgs transition in several three-dimensional lattice realizations of the noncompact CP$^1$ model (NCCP$^1$), a gauge theory with two complex matter fields with SU(2) invariance. By comparing with a one-component theory, which is well understood and has continuous transition in the inverted XY universality class, we argue that the two-component case also has continuous Higgs transition with a larger correlation length exponent (i.e., it is ``more continuous''). The transition can become first order in the vicinity of a new ``Molecular'' phase, which occurs in one of our models, but is continuous in a wide range of parameters away from this phase. The situation is significantly clarified by studying a model where the Molecular phase is entirely absent, and a wide regime with a continuous transition can be readily established. The two-component theory is also an effective description of the hedgehog-suppressed O(3) universality, and results are relevant for the recently discussed ``deconfined quantum criticality'' scenario for the continuous Valence Bond Solid to Neel quantum phase transition.
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A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.
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Charged Abelian Higgs phase transitions in three-dimensional compact lattice U(1) gauge models with multicharge scalar matter
Finite-size scaling analyses of Monte Carlo data for 3D compact lattice U(1) models with doubly-charged N-component scalars show continuous DC-OD transitions for N=10, weak first-order for N≤7, and inconclusive results for N=8,9, yielding the estimate N_cL=9(1).
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Coherent and dissipative dynamics at quantum phase transitions
A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.