  The criticality of the (2+1)-dimensional XY model is investigated with the
numerical diagonalization method. So far, it has been considered that the
diagonalization method would not be very suitable for analyzing the criticality
in large dimensions (d \ge 3); in fact, the tractable system size with the
diagonalization method is severely restricted. In this paper, we employ
Novotny's method, which enables us to treat a variety of system sizes
N=6,8,...,20 (N: the number of spins constituting a cluster). For that purpose,
we develop an off-diagonal version of Novotny's method to adopt the
off-diagonal (quantum-mechanical XY) interaction. Moreover, in order to improve
the finite-size-scaling behavior, we tune the coupling-constant parameters to a
scale-invariant point. As a result, we estimate the critical indices as
\nu=0.675(20) and \gamma/\nu=1.97(10).
