  Electronic flat bands represent a paradigmatic platform to realize strongly
correlated matter due to their associated divergent density of states. In
common instances, including electron-electron interactions leads to magnetic
instabilities for repulsive interactions and superconductivity for attractive
interactions. Nevertheless, interactions of Kondo nature in flat band systems
have remained relatively unexplored. Here we address the emergence of
interacting states mediated by Kondo lattice coupled to a flat band system.
Combining dynamical mean-field theory and tensor networks methods to solve flat
band Kondo lattice models in one and two dimensions, we show the emergence of a
robust underscreened regime leading to a magnetically ordered state in the flat
band. Our results put forward flat band Kondo lattice models as a platform to
explore the genuine interplay between flat band physics and many-body Kondo
screening.
