Renormalization group studies of the interplay between Kondo effect, valence fluctuations and topological order

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.