Ph.D Student | Khait Ilia |
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Subject | Dynamical Response Functions of Strongly Interacting Models |

Department | Department of Physics |

Supervisor | Professor Assa Auerbach |

Full Thesis text |

This dissertation contains two projects. First, the phenomenon of many body localization which has been a subject of intense investigation for the past few years both by theory and experiments. It arises from the interplay between interactions and disorder in low dimensional quantum systems.

The long-time dynamics of the delocalized phase was difficult to access with existing numerical tools, for example numerical diagonalization is limited to small systems. In this manuscript, we were the first to develop and apply the continued fraction representation to calculate response functions in the presence of disorder. This approach targets the thermodynamic limit directly and avoids boundary effects which plague other numerical schemes. We were able to obtain the sub-diffusive exponents of the conductivity and the dynamical auto-correlation functions to high accuracy. Our work settled a long-debated question whether a diffusive regime exists in the weak disorder regime of the Heisenberg model.

Using the same method, we numerically study dynamical response functions of strongly interacting fermions and bosons. One subject of our interest is transport properties such as electrical conductivity. It is a subject of much interest since it relates feasible experiments with pure theoretical predictions. We use models such as Hard Core Bosons that describe unconventional superconductors above the transition temperature such as cuprates and pnictides. We expand the Kubo formulae in the continued fraction representation. We start at infinite temperature and then generate higher orders in inverse temperature. The qualitative picture from the calculations can shed light on the applicability of the theoretical models on real materials.

The second project studies the one-dimensional Kondo lattice. The Kondo Lattice Model is an important unsolved model in condensed matter physics which describes heavy fermion materials. The essence of the model is a magnetic interaction between conduction electrons and localized magnetic moments. In any dimension, the difficulty of this model arises because of competing mechanisms which either favour or suppress magnetic order. Even the (a priori simple) one dimensional Kondo lattice remains a model without any analytic solution.

Using the density matrix renormalization group technique, I obtained the Tomonaga-Luttinger liquid exponents and momentum dependent charge and spin susceptibilities. This work settled the phase diagram in the weak coupling limit and proved the existence of a heavy Luttinger liquid phase with a large Fermi surface. Comparisons to large-$N$ (slave boson) mean field theory shed light on the physics of that phase. The main goal of this work is to come up with supporting evidence for a phenomenological field theoretic effective model that would capture the low energy physics.