Benchmark of the Polynomial Expansion Monte Carlo Method

Abstract

In this section, we present the benchmark of the polynomial expansion Monte Carlo method to a Kondo lattice model with classical localized moments on a geometrically frustrated lattice. We apply the method to the model in Eq. (7.1) introduced in Sect. 7.1.1, the spin-ice type Ising-spin Kondo lattice model on a three-dimensional pyrochlore lattice, and examine the convergence in terms of the order of polynomials and the truncation distance. We find that, in a wide range of electron density at a relatively weak Kondo coupling compared to the noninteracting bandwidth, the results by the polynomial expansion method show good convergence to those by the conventional method within reasonable numbers of polynomials. On the other hand, we also show that the real-space truncation is not helpful in reducing the calculation amount for the system sizes that we reached, as the sufficient convergence is obtained when most of the sites are involved within the truncation distance.