Abstract:

There are plenty of lattices in one, two, and three dimensions  which support a completely dispersionless (flat) one-particle energy band.  If the flat band happens to be the lowest-energy one,  it is possible to construct and completely characterize  a certain manifold of many-particle ground states  even in the presence of strong interactions.  These states determine the low-temperature properties  of strongly correlated systems  in a specific range of external parameters [1].  
In this talk I discuss the effect of slight dispersion of a previously strictly flat band.  I focus on the high-field low-temperature properties  of some quantum Heisenberg antiferromagnets [2] and on the kinetic-energy-driven ground-state ferromagnetism  in the standard Hubbard model at low electron densities [3].  I also discuss why these findings are useful  in searching for experimental manifestation of flat-band effects in strongly correlated systems.  
 
[1] O. Derzhko, J. Richter, and M. Maksymenko,  Int. J. Mod. Phys. B 29, 1530007 (2015).  
[2] O. Derzhko, J. Richter, O. Krupnitska, and T. Krokhmalskii,  Phys. Rev. B 88, 094426 (2013);  Low Temp. Phys. 40, 513 (2014);  J. Richter, O. Krupnitska, T. Krokhmalskii, and O. Derzhko,  J. Magn. Magn. Mater. 379, 39 (2015).  
[3] O. Derzhko and J. Richter,  Phys. Rev. B 90, 045152 (2014);  P. Müller, J. Richter, and O. Derzhko,  Phys. Rev. B 93, 144418 (2016).