Fixed-node Monte Carlo Method Research Articles

Fixed-node Monte Carlo calculations for the 1d Kondo lattice model

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 π, in agreement with earlier calculations.

Fixed-Node Monte Carlo Studies of Excitons in Confined Geometries

We study the properties of excitons in CEO quantum wires by the fixed-node Monte Carlo method in connection with recent experiments. The results of our calculations indicate that 1. as a function of the well width in a stem-arm symmetric structure at Al concentration of x = 0.3, the energy shift between the well and wire excitons reaches a peak value of about 25 meV at a well width of 25 Å; 2. the Coulomb interaction plays an important if not the dominant role. Depending on the well width, the correlated electron–hole Coulomb energy can be as large as 20 meV. The anisotropy in the projected density of the hole is significantly suppressed by electron–hole correlation; 3. the binding energy enhancement can be up to 70% at the optimal well widths; 4. there is more than one bound state in the center of mass motion of the exciton in the direction perpendicular to the quantum wire. This is markedly different from the single particle case where only one bound state exists; 5. comparison between our numerical results and experimental data show that the effective mass approximation with one hole band is sufficient for the computation of various energies of the exciton in typical experimental structures around well widths 70 Å.

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

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.