Deconfinement of Spinons on Critical Points: Multi-Flavor CP$^1$ + U(1) Lattice Gauge Theory in Three Dimensions

TL;DR

This study uses Monte-Carlo simulations to analyze a 3D multi-flavor CP$^1$ + U(1) lattice gauge theory, revealing a transition from confinement to deconfinement phases at high flavor numbers, which has implications for quantum spin models.

Contribution

The paper demonstrates that the phase structure on the critical line depends on the number of flavors, showing deconfinement for large Nf, advancing understanding of gauge dynamics in quantum spin systems.

Findings

Deconfinement occurs at Nf ≥ 14.

Confinement is observed for small Nf.

Gauge dynamics on the critical line varies with Nf.

Abstract

In this paper, we study the 3D $N_{\rm f}$-flavor CP$^1$ model (a set of $N_{\rm f}$ CP$^1$ variables) coupled with a dynamical compact U(1) gauge field by means of Monte-Carlo simulations. This model is relevant to 2D $s=1/2$ quantum spin models, and has a phase transition line which separates an ordered phase of global spin symmetry from a disordered one. From gauge theoretical point of view, the ordered phase is a Higgs phase whereas the disordered phase is a confinement phase. We are interested in the gauge dynamics just on the critical line, in particular, whether a Coulomb-like deconfinement phase is realized there. This problem is quite important to clarify low-energy excitations in certain class of quantum spin models. If the gauge dynamics is in the deconfinement phase there, spinons, which transform in the fundamental representation of the SU($N_{\rm f}$) symmetry, appear as low-energy excitations. By Monte-Carlo simulations, we found that the "phase structure" on the {\em criticality} strongly depends on the value of $N_{\rm f}$. For small $N_{\rm f}$, the confinement phase is realized, whereas the deconfinement phase appears for sufficient large $N_{\rm f}\ge 14$. This result strongly suggests that compact QED$_3$ is in a deconfinement phase for sufficiently large number of flavors of massless fermions.