Matter fields near quantum critical point in (2+1)-dimensional U(1) gauge theory

TL;DR

This paper investigates the behavior of matter fields near a quantum critical point in a (2+1)-dimensional U(1) gauge theory, focusing on confinement, deconfinement, and physical properties at criticality.

Contribution

It provides a detailed analysis of the phase transition, confinement, and dynamical mass generation of matter fields in the gauge theory at the quantum critical point.

Findings

Matter fields are deconfined at the quantum critical point r=0.

Dynamical fermion mass depends on flavor number and scalar boson mass.

Specific heat and susceptibility can indicate the quantum critical point.

Abstract

We study chiral phase transition and confinement of matter fields in (2+1)-dimensional U(1) gauge theory of massless Dirac fermions and scalar bosons. The vanishing scalar boson mass, $r=0$, defines a quantum critical point between the Higgs phase and the Coulomb phase. We consider only the critical point $r=0$ and the Coulomb phase with $r > 0$. The Dirac fermion acquires a dynamical mass when its flavor is less than certain critical value $N_{f}^{c}$, which depends quantitatively on the flavor $N_{b}$ and the scalar boson mass $r$. When $N_{f} < N_{f}^{c}$, the matter fields carrying internal gauge charge are all confined if $r \neq 0$ but are deconfined at the quantum critical point $r = 0$. The system has distinct low-energy elementary excitations at the critical point $r=0$ and in the Coulomb phase with $r \neq 0$. We calculate the specific heat and susceptibility of the system at $r=0$ and $r \neq 0$, which can help to detect the quantum critical point and to judge whether dynamical fermion mass generation takes place.