  We examine Gaussian-basis Monte Carlo method (GBMC) introduced by Corney and
Drummond. This method is based on an expansion of the density-matrix operator
rho by means of the coherent Gaussian-type operator basis Lambda and does not
suffer from the minus sign problem. The original method, however, often fails
in reproducing the true ground state and causes systematic errors of calculated
physical quantities because the samples are often trapped in some metastable or
symmetry broken states. To overcome this difficulty, we combine the
quantum-number projection scheme proposed by Assaad, Werner, Corboz, Gull and
Troyer in conjunction with the importance sampling of the original GBMC method.
This improvement allows us to carry out the importance sampling in the
quantum-number-projected phase-space. Some comparisons with the previous
quantum-number projection scheme indicate that, in our method, the convergence
with the ground state is accelerated, which makes it possible to extend the
applicability and widen the range of tractable parameters in the GBMC method.
The present scheme offers an efficient practical way of computation for
strongly correlated electron systems beyond the range of system sizes,
interaction strengths and lattice structures tractable by other computational
methods such as the quantum Monte Carlo method.
