We use a real-space slave-rotor theory of the physics of topological Mott insulators, using
the Kane-Mele-Hubbard model as an example, and show that a topological gap in the …

We analyze the role of spatial electronic correlations and, in particular, of the magnetic
fluctuations in Mott insulators. A half-filled Hubbard model is solved at large strength of the …

Recent advancements in moir\'e engineering motivate study of the behavior of strongly-
correlated electrons subject to substantial orbital magnetic flux. We investigate the triangular …

Despite the tremendous interest raised by the recent realization of magnetic Weyl
semimetals and the observation of giant anomalous Hall signals, most of the theories used …

Symmetry protected topological (SPT) phases are fundamental quantum many-body states
of matter beyond Landau's paradigm. Here, we introduce the concept of quantum restored …

We investigate the emergence of topological features in the charge excitations of Mott
insulators in the Chern-Hubbard model. In the strong correlation regime, treating electrons …

Anomaly analysis has been an important and powerful tool in studying nonperturbative
physics for decades. The anomaly inflow mechanism provides an intuitive interpretation of …

We present a model in which a Hatsugai-Kohmoto interaction is added to a system of
fermions with a Weyl point in their non-interacting dispersion relation, and analyze its …

This thesis is based on research conducted in Prof. Qimiao Si's group. Parts of the work
were performed in collaboration with Prof. Jennifer Cano's group at Stony Brook University …