Interaction and disorder effects on topology in one-dimensional lattices

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The topological phases and phase transitions in condensed matter is subject of great interest in the field of condensed matter physics. Starting from the first observation of the quantum Hall effect in two dimensional electron systems, study of topological phases has attracted a great deal of attention in the last several decades. Topological phases are characterised by gapped bulk spectrum and gapless or localized edge states, non-local correlations and well defined topological invariants. A class of topological phases which is known as the symmetry protected topological phases where the bulk-boundary correspondence is protected by some underlying symmetries. In general the topological character is robust to perturbation although strong perturbation such as interaction and disorder breaks down the topological nature. However, in certain cases, these perturbations can drive a topological phase transition or may induce a topological character in the system. Due to the rapid progress in the field of quantum simulations of such systems in artificial experimental setups and their relevance as effective models to some of the real materials, these systems are explored in various different contexts. Motivated by this development, we focus on the study of interaction and disorder effects on the topological character of low dimensional lattice systems in this thesis.
Supervisors: Pandey, Kanhaiya and Mishra, Tapan