The study of strong correlations in quantum many-body systems reveals emergent properties not explained by conventional theories like electronic band theory. My work delves into two fundamental directions
within the realm of strongly correlated quantum systems. First, it explores designer lattices with flat electronic bands, focusing on the impact
of strong correlations on phases and phase transitions in two-dimensional
systems. These designer lattices, enabled by advances in ultracold atomic
gases, photonic crystals, and solid-state systems, offer unique electronic
properties due to their quenched energy states. Special attention is given
to systems like the Lieb lattice, exemplifying enhanced correlations and
novel electronic phenomena.
The second part of my work delves into systems with competing interaction scales, emphasizing the interplay of disorder and interactions in
quantum many-body systems. This exploration reveals how interaction
modifies the Anderson localization transition in the presence of disorder,
leading to novel quantum phases. This piece of work concentrates on the
interplay of superconductivity, spin-orbit coupling, and disorder, as well
as itinerant magnetism, spin-orbit coupling, and disorder. These investigations promise insights into unconventional quantum phases induced
by disorder and interaction, a subject gaining prominence in condensed
matter physics. As a future plan, I have introduced the Landau-GinzburgWilson (LGW) theory for multiband superconductors.
Ultimately, my work aims to numerically engineer and comprehend
the effects of strong correlations in systems with flat electronic bands and
competing interaction scales. By investigating such systems, this research
contributes to the evolving understanding of strongly correlated quantum
phenomena and their potential applications.