Title: Thermodynamic properties of Ba$_2$CoSi$_2$O$_6$Cl$_2$ in strong magnetic field: Realization of flat-band physics in a highly frustrated quantum magnet,
Abstract: The search for flat-band solid-state realizations is a crucial issue to
verify or to challenge theoretical predictions for quantum many-body flat-band
systems. For frustrated quantum magnets flat bands lead to various
unconventional properties related to the existence of localized many-magnon
states. The recently synthesized magnetic compound Ba$_2$CoSi$_2$O$_6$Cl$_2$
seems to be an almost perfect candidate to observe these features in
experiments. We develop a theory for Ba$_2$CoSi$_2$O$_6$Cl$_2$ by adapting the
localized-magnon concept to this compound. We first show that our theory
describes the known experimental facts and then we propose new experimental
studies to detect a field-driven phase transition related to a
Wigner-crystal-like ordering of localized magnons at low temperatures.