Executive Summary : | This proposal brings together two seemingly disparate pillars of quantum condensed matter physics, namely, strong electron correlation and topology. While the concept of topology has been prevalent in physics since decades, it came into prominence with the discovery of topological insulators and topological phase transitions. Nevertheless, the concepts have been mostly confined to non-interacting systems. For interacting systems standard topological classification breaks down and development of new approaches deem necessary. This proposal builds upon one of the recent works of the PI (Phys. Rev. B 102, 081110 (R) (2020) (Editors' Suggestion)) that overcomes this conceptual hindrance by use of a new, auxiliary fermion mapping of the interacting system to a non-interacting system. This proposal will go well beyond this work by encompassing general parameter regimes and developing a connection with entanglement entropy measure. The latter appears to be a powerful lens for probing quantum phase transitions and has recently been utilised in studying the Mott transition in the two dimensional Hubbard model. The theoretical approach developed in this proposal may not be just limited to Mott metal-insulator transitions but can be used as a conceptual tool to analyse any strong-correlation driven metal-insulator transition. In summary, this proposal will explore emergent topology in strong correlation driven metal-insulator transitions and provide new insights by building a connection via entanglement entropy calculations across the quantum phase transition using state-of-the-art computational many-body techniques. This unique approach has not been attempted before in the literature. It is believed, that the projects undertaken here will present a carefully prepared plan of action resulting in high profile publications. |