| Summary: | Two aspects of strongly correlated electron systems are studied in this thesis.
Hubbard-type models are thought to be at the basis of high-critical-temperature superconductivity.
One interaction which has not had much study is the nearest-neighbour
hopping of on-site singlet pairs. We refine earlier renormalization group arguments and,
using the density-matrix renormalization group method, numerically confirm their prediction
that a spin gap opens at infinitesimal pair-hopping amplitude V > 0 in the
one-dimensional tight-binding model. We also find a phase separation transition at a
finite V > 0 as well as a spin-gap transition at a finite V < 0.
The exotic magnetic behaviour of heavy-fermion materials involves an interplay between
the screening of local moments from each other and the formation of a magnetic
state of long range order. While the single-impurity Kondo Hamiltonian is thought to
model some aspects of this behaviour, the properties of the Kondo lattice model away
from half-filling are largely unknown. We determine the presence of a spin-gap region
in the phase diagram of the one-dimensional Heisenberg-Kondo lattice model and make
predictions about certain concealed dimerization order parameters. === Science, Faculty of === Physics and Astronomy, Department of === Graduate
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