Polynomial expansion method for the Monte Carlo calculation of strongly correlated electron systems

We present a new Monte Carlo algorithm for a class of strongly correlated electron systems where electrons are strongly coupled to thermodynamically fluctuating classical fields. As an example, the method can be applied to electron-spin coupled systems such as the double-exchange model and dilute magnetic semiconductors, as well as electron-phonon systems. In these systems, calculation of the Boltzmann weights involves quantum-mechanical treatments for the electronic degrees of freedom. The traditional method requires all eigenvalues of the electronic Hamiltonian through a matrix diagonalization. Here we demonstrate that the Boltzmann weight can be obtained by matrix products and trace operations, if the calculation of the density of states is performed through a moment expansion using the Chebyshev polynomials of the Hamiltonian matrix. Therefore, the polynomial expansion method provides a faster calculation for the Boltzmann weights on large-size systems. We also show some results for the application of this algorithm to the study of critical phenomena in the simplified double-exchange model.