  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.
