Fixed-Node Monte Carlo Calculations for the 1d Kondo Lattice Model

TL;DR

This paper evaluates the Fixed-Node Quantum Monte Carlo method on the 1D Kondo lattice model, demonstrating its effectiveness in estimating ground state energies and spin correlations despite the sign problem.

Contribution

It applies and tests the Fixed-Node Monte Carlo method to the 1D Kondo lattice, providing detailed implementation and validation against exact results.

Findings

Fixed-Node estimates closely match exact ground state energies.

Spin correlation functions are reasonably accurate.

The method successfully calculates the spin gap and excitation spectrum.

Abstract

The effectiveness of the recently developed Fixed-Node Quantum Monte Carlo method for lattice fermions, developed by van Leeuwen and co-workers, is tested by applying it to the 1D Kondo lattice, an example of a one-dimensional model with a sign problem. The principles of this method and its implementation for the Kondo Lattice Model are discussed in detail. We compare the fixed-node upper bound for the ground state energy at half filling with exact-diagonalization results from the literature, and determine several spin correlation functions. Our `best estimates' for the ground state correlation functions do not depend sensitively on the input trial wave function of the fixed-node projection, and are reasonably close to the exact values. We also calculate the spin gap of the model with the Fixed-Node Monte Carlo method. For this it is necessary to use a many-Slater-determinant trial state. The lowest-energy spin excitation is a running spin soliton with wave number pi, in agreement with earlier calculations.