▁of ▁an ▁imp urity , ▁and ▁ ▁corresponds ▁to ▁a ▁condu ction ▁electron ▁anni h ilation ▁operator , ▁and ▁ ▁labels ▁the ▁spin . ▁The ▁on – site ▁C oul omb ▁rep ulsion ▁is ▁, ▁which ▁is ▁usually ▁the ▁dominant ▁energy ▁scale , ▁and ▁ ▁is ▁the ▁ho pping ▁strength ▁from ▁site ▁ ▁to ▁site ▁. ▁A ▁significant ▁feature ▁of ▁this ▁model ▁is ▁the ▁hy brid ization ▁term ▁, ▁which ▁allows ▁the ▁ ▁electrons ▁in ▁heavy ▁ferm ion ▁systems ▁to ▁become ▁mobile , ▁although ▁they ▁are ▁separated ▁by ▁a ▁distance ▁greater ▁than ▁the ▁Hill ▁limit . ▁ ▁For ▁heavy - fer m ion ▁systems , ▁a ▁lattice ▁of ▁imp ur ities ▁is ▁described ▁by ▁the ▁periodic ▁Anderson ▁model : ▁ ▁There ▁are ▁other ▁variants ▁of ▁the ▁Anderson ▁model , ▁for ▁instance ▁the ▁SU ( 4 ) ▁Anderson ▁model , ▁which ▁is ▁used ▁to ▁describe ▁imp ur ities ▁which ▁have ▁an ▁orb ital , ▁as ▁well ▁as ▁a ▁spin , ▁degree ▁of ▁freedom . ▁This ▁is ▁relevant ▁in ▁carbon ▁nan ot ube ▁quantum ▁dot ▁systems . ▁The ▁SU ( 4 ) ▁Anderson ▁model ▁Hamiltonian ▁is ▁ ▁where ▁ ▁and ▁ ▁label ▁the ▁orb ital ▁degree ▁of ▁freedom ▁( which ▁can ▁take ▁one ▁of ▁two ▁values ), ▁and ▁ ▁represents ▁a ▁number ▁operator . ▁ ▁See ▁also ▁▁ ▁K ondo ▁effect ▁ ▁K ondo ▁model ▁ ▁Anderson ▁local ization ▁ ▁References ▁▁▁▁▁▁ ▁Category : Quant um ▁L attice ▁models ▁Category : Cond ensed ▁matter ▁physics <0x0A> </s> ▁Th ym ine ▁g ly col ▁( 5