  We apply the recursive stochastic state selection method, which is a new
method for Monte Carlo study we have recently developed, to quantum spin
systems with positive definite Hamiltonians. Through numerical studies of
two-dimensional J1-J2 Heisenberg model on a square lattice with unfrustrated
couplings J1=1 and J2=-1 and with non-frustrated ones J1=1 and J2=0, we find
that a kind of equilibrium is realized in these systems. We also observe that
in this equilibrium we can obtain a quite accurate estimate of the energy
eigenvalue for the system's ground state. Statistical relative errors in our
results are 0.03% for the 36-site unfrustrated model and 0.06% for the 64-site
non-frustrated model.
