Abstract:
Strongly correlated electron systems(SCES) comprise a range of materials which
exhibit panorama of exotic and emergent behaviour. These systems include Mott
insulators, high Tc superconductors, heavy fermion systems, spin liquids, magnetic
materials, fractional quantum Hall fluids. Band theory, based entirely on the quantum
theory of solids which have periodic lattice structures, has been a huge success
because of the broad range of solid state systems whose transport properties were
understood based on this theory. But when it comes to strongly correlated electron
systems, band theory fails. The Mott insulating state and Anderson insulators are
just two examples which can not be explained on the basis of band theory because
there are new physical principles at work. The principles of quantum many-body
systems were laid out by many pioneers of this field including Landau, Anderson and
Wilson. These principles include adiabatic continuity on which is based Fermi liquid
theory, Spontaneous symmetry breaking which is the paradigm for understanding
the ordered states of matter, Renormalization group which is the natural framework
to study the effects of strong interactions. These principles have been discussed at
length in a very beautiful book by Anderson[1]. In this thesis, we have employed
renormalization group methods to study the interplay between Kondo effect, valence
fluctuations and topological order.
