  We present the benchmark of the polynomial expansion Monte Carlo method to a
Kondo lattice model with classical localized spins on a geometrically
frustrated lattice. The method enables to reduce the calculation amount by
using the Chebyshev polynomial expansion of the density of states compared to a
conventional Monte Carlo technique based on the exact diagonalization of the
fermion Hamiltonian matrix. Further reduction is brought by a real-space
truncation of the vector-matrix operations. We apply the method to the model
with spin-ice type Ising spins on a three-dimensional pyrochlore lattice, and
carefully 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. This enables
us to study the systems up to 4x8^3 = 2048 sites, while the previous study by
the conventional method was limited to 4x4^3 = 256 sites. On the other hand,
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. The
necessary truncation distance, however, appears not to show significant system
size dependence, suggesting that the truncation method becomes efficient for
larger system sizes.
