A new quantum Monte-Carlo method, efficient for systems with diagonal-dominated Hamiltonians, is proposed. The eigenstates are found by diagonalization of the Hamiltonian in a truncated basis generated by a Monte-Carlo algorithm. The method is applied to the problem of the quantum melting of a Wigner crystal on a lattice. Arguments are given that this is a second order phase transition and a connection between the melting and the distribution of the lowest energy levels is demonstrated.

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