Study of strongly correlated one-dimensional systems with long-range interactions

During this Ph.D, we studied one-dimensional systems with long-range couplings. In the first part, we demonstrate that power-law couplings lead to an algebraic decay of correlations at long distances in disordered quantum wires. In the second chapter, we analyzed an extended Hubbard model where particles interact via a finite-range potential that induces frustration and new exotic phases. In the third chapter, we demonstrated that restoring energy extensivity has an influence on the low-energy properties of quantum model in the thermodynamic limit. Finally, we provide preliminary results on the modification of Anderson localization due to the coupling to a cavity mode.