Band flatness optimization through complex analysis

Understand

Narrow band electron systems are particularly likely to exhibit correlated many-body phases driven by interaction effects.

• Examples include magnetic materials, heavy fermion systems, and topological phases such as fractional quantum Hall states and their lattice-based cousins, the fractional Chern insulators (FCIs).
• Here we discuss the problem of designing models with optimal band flatness, subject to constraints on the range of electron hopping.
• In particular, we show how the imaginary gap, which serves as a proxy for band flatness, can be optimized by appealing to Rouche's theorem, a familiar result from complex analysis.