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

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 $r\mathrm{\ne }0$ 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 $r \neq 0$\mathrm{.}Wecalculatethespecificheatandsusceptibilityofthesystemat$r=0$and$r \neq 0$, which can help to detect the quantum critical point and to judge whether dynamical fermion mass generation takes place.