Polynomial Expansion Monte Carlo Study of Frustrated Itinerant Electron Systems: Application to a Spin-ice type Kondo Lattice Model on a Pyrochlore Lattice

TL;DR

This study benchmarks a polynomial expansion Monte Carlo method for a frustrated Kondo lattice model on a pyrochlore lattice, demonstrating its efficiency and convergence for larger system sizes compared to traditional methods.

Contribution

It introduces and validates a polynomial expansion Monte Carlo approach with real-space truncation for large-scale frustrated electron systems, enabling more efficient simulations.

Findings

Good convergence of the polynomial method within reasonable polynomial orders.

The method allows simulation of systems up to 2048 sites, larger than previous studies.

Truncation distance shows little dependence on system size, indicating scalability.

Abstract

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.