Executive Summary : | Study of topological phase transition is one of the most fascinating areas of research in the field of modern quantum condensed matter physics that does not belong to the standard Landau-Ginzberg paradigm of spontaneous symmetry breaking. After the seminal observation of the quantum Hall effect, the thrust for understanding and realizing topological phase transitions in various systems have led to unravelling a wealth of novel phenomena in recent years. Characterised by their non-trivial features such as gapped bulk spectrum, gapless edge or surface states and non-local orders, the research on topological phases of matter have gained enormous attention recently in the context of fundamental physics as well as quantum technologies. These phases can be described by a system which requires a unique ground state with gapped excitation bulk and non-trivial edge/surface states that are protected by certain underlying symmetry (ies). A TPT between two topologically distinct gapped phases can be carried out by either breaking the symmetry or by closing the bulk gap (and thus by breaking the adiabaticity). Also since interactions are an inevitable part of real materials, the interplay between topology and strong interaction gives rise to some striking questions. Can the topological phenomena of free fermions survive interactions? More interestingly, can a system exhibit an SPT phase with the inclusion of interactions even though its non-interacting counterpart is devoid of any topological signatures? In this proposal we aim to address some of the important and timely problems on interaction effects on topological phase transitions. Our proposal is based on three main objectives such as (1) Symmetry-protected topological phase transition induced via non-local interactions. 2) Topological properties of interacting particles on a multi-band lattice. 3) Frustration- and interaction-induced topological phase transition. These problems with be solved using the analytical method known as the bosonization technique which constitutes a systematic mapping of a fermionic system operators and the states into bosonic ones making them more suitable for the understanding of the physics of the system, sometimes even allowing for an exact solution. For all the case we will complement the results with the analysis based on state-of-the art density matrix renormalization (DMRG) methods. |