Fixed-node Monte Carlo study of the two-dimensional Hubbard model

Abstract

The fixed-node Monte Carlo method is extended to lattice fermion models. This method replaces the problem of finding the ground state of a many-fermion system by an effective eigenvalue problem of finding the lowest-energy wave function in a given region of the configuration space. It has previously only been applied to fermions moving in continuous space. The discreteness of the configuration space causes the algorithm to differ from that of the continuum. The method is tested against a known limiting case where exact results are available for comparison. Good agreement is found. Using the fixed-node Monte Carlo method, we study the domain-wall phase in the ground state of the two-dimensional Hubbard model. The existence of a domain-wall phase which has domains of antiferromagnetic phases separated by walls of holes is recently suggested by inhomogeneous Hartree-Fock (HF) and variational Monte Carlo (VMC) calculations. Large improvements of the energies are found. The domain walls are broader than those obtained by the HF and VMC calculations.