CP^1+U(1) Lattice Gauge Theory in Three Dimensions: Phase Structure, Spins, Gauge Bosons, and Instantons

TL;DR

This study investigates a 3D lattice CP^1+U(1) gauge model, revealing a phase transition between Higgs and confinement phases, with detailed analysis of instantons, gauge bosons, and critical behavior relevant to quantum spin systems.

Contribution

The paper provides the first detailed numerical analysis of the phase structure of a 3D CP^1+U(1) lattice gauge theory, including the nature of the phase transition and instanton effects.

Findings

Identified a second-order phase transition between Higgs and confinement phases.

Discovered a crossover within the confinement phase separating dense and dilute instanton regions.

Found that gauge bosons remain massive on the critical line, indicating confinement at criticality.

Abstract

In this paper we study a 3D lattice spin model of CP$^1$ Schwinger-bosons coupled with dynamical compact U(1) gauge bosons. The model contains two parameters; the gauge coupling and the hopping parameter of CP$^1$ bosons. At large (weak) gauge couplings, the model reduces to the classical O(3) (O(4)) spin model with long-range and/or multi-spin interactions. It is also closely related to the recently proposed "Ginzburg-Landau" theory for quantum phase transitions of $s=1/2$ quantum spin systems on a 2D square lattice at zero temperature. We numerically study the phase structure of the model by calculating specific heat, spin correlations, instanton density, and gauge-boson mass. The model has two phases separated by a critical line of second-order phase transition; O(3) spin-ordered phase and spin-disordered phase. The spin-ordered phase is the Higgs phase of U(1) gauge dynamics, whereas the disordered phase is the confinement phase. We find a crossover in the confinement phase which separates dense and dilute regions of instantons. On the critical line, spin excitations are gapless, but the gauge-boson mass is {\it nonvanishing}. This indicates that a confinement phase is realized on the critical line. To confirm this point, we also study the noncompact version of the model. A possible realization of a deconfinement phase on the criticality is discussed for the CP$^N$+U(1) model with larger $N$.