  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.
