Study of the Hall effect in two different strongly correlated fermion systems

This thesis investigates the Hall effect across two distinct strongly correlated fermion systems, leveraging theoretical models to explore the underlying mechanisms of charge transport in these complex materials. The objective is to deepen the understanding of the Hall effect in low-dimensional systems and its dependence on the nature of the strong correlations. Employing a combination of analytical methods, including linear response theory and Kubo formulas, as well as numerical simulations, we assess the behaviors of the Hall constant in various geometries and dimensionalities. The results reveal significant differences in the Hall response influenced by dimensionality and correlation strength, highlighting the nuanced interplay between magnetic fields and the dynamical response of these systems. Notably, specific cases, such as the quasi one-dimensional organic conductors, are examined in detail, providing insight into their unique transport characteristics under the Hall effect. This work contributes to the broader field of condensed matter physics by elucidating the rich physics of correlated electrons and their manifestations in transport phenomena. The findings have implications for future experimental studies and the design of novel materials with tailored transport properties.