### Interacting Quantum Systems: Topological Phenomena and Effective Theories

Project Type: Prin 2022

Funded by: MUR

Period: Sep 28, 2023 – Sep 28, 2025

Budget: €75.620,00

Principal Investigator: Domenico Monaco (Sapienza Università di Roma)

Local coordinator: Chiara Boccato (Università di Pisa)

##### Description

The project will employ and develop tools from mathematical physics to study interacting quantum matter, focusing on its topological phases and its description through effective theories. Since the discovery of the integer and fractional quantum Hall effects and with the classification of topological insulators, the role of geometry and topology in condensed matter physics has been rapidly promoted to a fundamental paradigm, and it is nowadays a booming area of research. Mathematical physics, in particular the mathematical methods developed to treat quantum mechanics, provides the natural framework for the analysis of these phenomena. While we have a clear understanding of topological phases of matter in the 1-body approximation, the challenge for the near future is the comprehension of the interplay between topological effects and interactions among quantum particles. In typical condensed matter systems, the number of particles involved is huge, thus requiring the formulation of effective theories which describe their behavior in terms of fewer degrees of freedom. One of the most renowned examples is the cold Bose gas and its condensation, deeply related to the emergence of superfluidity and superconductivity in fermionic systems. From the point of view of mathematics, it appears that the techniques and effective theories used to describe many-body quantum systems will also play a crucial role in the analysis of topological phases. A clear mathematical description of these physical systems will in the long term also help in the development of new technologies, for example in quantum computation or solid-state memory devices.