  In this paper we shall introduce a lattice model of unconventional
superconductors (SC) like d-wave SC in order to study quantum phase transition
at vanishing temperature ($T$). Finite-$T$ counterpart of the present model was
proposed previously with which SC phase transition at finite $T$ was
investigated. The present model is a noncompact U(1) lattice-gauge-Higgs model
in which the Higgs boson, the Cooper-pair field, is put on lattice links in
order to describe d-wave SC. We first derive the model from a microscopic
Hamiltonian in the path-integral formalism and then study its phase structure
by means of the Monte Carlo simulations. We calculate the specific heat,
monopole densities and the magnetic penetration depth (the gauge-boson mass).
We verified that the model exhibits a second-order phase transition from normal
to SC phases. Behavior of the magnetic penetration depth is compared with that
obtained in the previous analytical calculation using XY model in four
dimensions. Besides the normal to SC phase transition, we also found that
another second-order phase transition takes place within the SC phase in the
present model. We discuss physical meaning of that phase transition.
