Strongly correlated fermions on frustrated lattices

Systems with frustrated interactions are generally characterized by a high density of low--lying excitations which leads to a high susceptibility and thus interesting physical effects. We study a novel class of strongly correlated fermions on frustrated lattices which allows for excitations which carry fractional charges [1]. For a systematic study, we firstly consider a model of spinless fermions on a geometrically frustrated planar pyrochlore (checkerboard) lattice. An effective Hamiltonian is derived for the strongly correlated limit which describes the low--lying excitations. We solve the fermionic sign problem for the latter Hamiltonian and thus make it possible to apply quantum Monte Carlo methods [3]. The ground state is shown to be charged ordered and fractional charges are linearly confined. Secondly, we consider a model of spinful fermions on the kagome lattice and study the interplay between charge -- and spin -- degrees of freedom. [1] P.~Fulde, K.~Penc, and N.~Shannon, Annalen der Physik {\bf 11}, 892 (2002) [2] E.~Runge and P.~Fulde, Phys. Rev. B {\bf 70}, 245113 (2004) [3] F.~Pollmann, J.~J.~Betouras, K.~Shtengel, and P.~Fulde, Phys. Rev. Lett. \textbf{97}, 170407 (2006)