Study of the One- and Two-Band Models for Colossal Magnetoresistive Manganites Using the Truncated Polynomial Expansion Method

Considerable progress has been recently made in the theoretical understanding of the colossal magnetoresistance (CMR) effect in manganites. The analysis of simple models with two competing states and a resistor network approximation to calculate conductances has confirmed that CMR effects can be theoretically reproduced using non-uniform clustered states. In this paper, the recently proposed Truncated Polynomial Expansion method (TPEM) for spin-fermion systems is tested using the double-exchange one-band, with finite Hund coupling $J_{\rm H}$, and two-band, with infinite $J_{\rm H}$, models. Two dimensional lattices as large as 48$\times$48 are studied, far larger than those that can be handled with standard exact diagonalization (DIAG) techniques for the fermionic sector. The clean limit (i.e. without quenched disorder) is here analyzed in detail. Phase diagrams are obtained, showing first-order transitions separating ferromagnetic metallic from insulating states. A huge magnetoresistance is found at low temperatures by including small magnetic fields, in excellent agreement with experiments. However, at temperatures above the Curie transition the effect is much smaller confirming that the standard finite-temperature CMR phenomenon cannot be understood using homogeneous states. By comparing results between the two methods, TPEM and DIAG, on small lattices, and by analyzing the systematic behavior with increasing cluster sizes, it is concluded that the TPEM is accurate to handle realistic manganite models on large systems. Our results pave the way to a frontal computational attack of the colossal magnetoresistance phenomenon using double-exchange like models, on large clusters, and including quenched disorder.