Finite-size scaling with modified boundary conditions

An efficient scheme is introduced for a fast and smooth convergence to the thermodynamic limit of electronic properties obtained with finite-size calculations on correlated Hamiltonians. This is obtained by modifying the energy levels of the free electron part of the Hamiltonian in a way consistent with the corresponding one-particle density of states in the thermodynamic limit. After this modification, free electron ground state energies, exact in the thermodynamic limit, are obtained with finite-size calculations and for all the particular fillings that satisfy the so called "closed-shell condition." For those fillings the auxiliary field quantum Monte Carlo technique is particularly efficient and, by combining it with the present method, we provide strong numerical evidence that phase separation occurs in the low doping region and moderate Uâ?4t regime of this model.