Four-dimensional CP$^1+$ U(1) lattice gauge theory for 3D antiferromagnets: Phase structure, gauge bosons and spin liquid

TL;DR

This study uses Monte Carlo simulations to explore the phase structure of a 3D lattice CP^1 + U(1) gauge model, revealing Higgs, Coulomb, and confinement phases relevant to antiferromagnets and high-Tc cuprates.

Contribution

It provides the first detailed phase diagram of the 3D CP^1 + U(1) lattice gauge theory with insights into magnetic phases and gauge boson properties.

Findings

Identified Higgs, Coulomb, and confinement phases.

Measured gauge boson mass and spin excitation gaps.

Discussed implications for high-Tc cuprate magnetic properties.

Abstract

In this paper we study the lattice CP$^1$ model in (3+1) dimensions coupled with a dynamical compact U(1) gauge field. This model is an effective field theory of the $s={1 \over 2}$ antiferromagnetic Heisenberg spin model in three spatial dimensions. By means of Monte Carlo simulations, we investigate its phase structure. There exist the Higgs, Coulomb and confinement phases, and the parameter regions of these phases are clarified. We also measure magnetization of O(3) spins, energy gap of spin excitations, and mass of gauge boson. Then we discuss the relationship between these three phases and magnetic properties of the high-$T_{\rm c}$ cuprates, in particular the possibility of deconfined-spinon phase. Effect of dimer-like spin exchange coupling and ring-exchange coupling is also studied.