Flat Bands: Design, Topology, and Correlations

Emergence of strongly correlated phases of matter is particularly probable in systems that exhibit an extensive degeneracy in
the absence of inter-particle interactions. The resulting quenching of kinetic energy, colloquially termed ’flat bands’, enhances
the efficacy of interactions and leads to interesting phases with both conventional broken symmetries, such as ferromagnets,
as well as topologically ordered phases such as lattice versions of fractional quantum Hall states and fractional topological
insulators. A flurry of recent numerical observations of fractionalized phases in lattice models with ’topological’ flat bands,
has renewed interest in the study of flat bands of electronic insulators. There have also been various proposals to realize
and study flat bands in experimental systems, ranging from oxide heterostructures to optical lattices of ultracold fermions
with an artificial gauge field. In a different vein, the realization of various frustrated hopping models of ultracold bosons in
optical lattices has motivated interest in the rather less well-studied problem of bosons in flat bands. In all these cases, the
fundamental role played by correlations simultaneously leads to novel behavior while complicating the understanding of these
phases from numerical and analytical approaches.

This focused workshop aims to bring together researchers working on diverse aspects of flat band physics, covering questions
such as: Is there a reliable route to designing flat bands in experimentally relevant systems, be they electronic or cold atomic
systems? What correlated phases and new physical phenomena can occur (generically or as a result of careful fine-tuning)?
Is there a systematic understanding and/or classification of (topological) phases in flat bands, and how does one characterise
them?