Comparative study of Higgs transition in one-component and two-component lattice superconductor models

TL;DR

This study uses Monte Carlo simulations to compare Higgs transitions in one- and two-component lattice superconductor models, revealing the two-component case generally exhibits continuous transitions with larger correlation length exponents, relevant for deconfined quantum criticality.

Contribution

It demonstrates that the two-component NCCP^1 model typically has a continuous Higgs transition, clarifies the role of the Molecular phase, and connects results to deconfined quantum criticality scenarios.

Findings

Two-component models generally show continuous Higgs transitions.

The transition can become first order near the Molecular phase.

A model without the Molecular phase exhibits a wide continuous transition regime.

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.