| In this thesis, we used a recently developed quantum Monte Carlo algorithm to study Anderson and Kondo Hamiltonians, models of magnetic ions interacting with a conduction or conduction-like band. These Hamiltonians are particularly relevant to "heavy fermion" materials, materials with anomalously high low-temperature susceptibilities and specific heats. One of the main purposes of our thesis is to gain some understanding of the magnetic properties of such systems.; We begin in the first two chapters by analyzing the one systematic approximation in the algorithm we use, the so-called "Trotter approximation." We show the vanishing of the leading error term under quite general conditions, and derive the form of the next-order term, enabling one to extrapolate in a controlled way to the exact limit. We then simulate systems of increasing complexity: first, a single magnetic ion impurity interacting with a conduction band; then, two impurities; and, finally, a lattice of regularly spaced magnetic ions, interacting with a conduction band.; We investigate in particular the competition between the "Kondo effect," which tends to quench the magnetic moments of the ions, and "RKKY" interactions between the ions, which can lead to long-range magnetic order in a lattice. We parameterize the general magnetic behavior of the different Hamiltonians we study, and discuss the implications of our results of heavy fermion materials. |
