Calculation of Dynamical and Many-Body Observables with the Polynomial Expansion Method for Spin-Fermion Models

The calculation of twoand four-particle observables is addressed within the framework of the truncated polynomial expansion method (TPEM). The TPEM replaces the exact diagonalization of the one-electron sector in models for fermions coupled to classical fields such as those used in manganites and diluted magnetic semiconductors. The computational cost of the algorithm is O(N) – with N the number of lattice sites – for the TPEM which should be contrasted with the computational cost of the diagonalization technique that scales as O(N). By means of the TPEM, the density of states, spectral function and optical conductivity of a double-exchange model for manganites are calculated on large lattices and compared to previous results and experimental measurements. The ferromagnetic metal becomes an insulator by increasing the direct exchange coupling that competes with the double exchange mechanism. This metal-insulator transition is investigated in three dimensions.