Oneofthemanyfascinatingaspectsofstronglycorrelatedelectronsystemsisthe appearanceoflowenergyscales: interestingphysicalphenomenaareobservedon anenergy(andtemperature)scalemuchlowerthane.g.localCoulombrepulsion, hybridization. etc. Well known examples are heavy fermion compounds and systemsinthevicinityofametal-insulatortransition. Thesephenomenacanbe describedusingsimple(butneverthelessstronglycorrelated)electronicmodels. Forthese models. the greatdifferenceinenergyscalesingeneralrepresentsa difficulttaskfor the theoretical investigation. Thenumerical renorrnalization groupmethodturnsouttobeaveryefficienttooltodealwiththeseproblems. ThismethodwasdevelopedbyWilsonfortheinvestigationoftheKondomodel andhasbeenrecently(successfully)appliedtolatticemodels(suchasHubbard modelandperiodicAndersonmodel)withinthedynamicalmeanfieldtheory.
We consider the SU (m|n) supersymmetric generalization of the one-dimensional SU (2|2) symmetric extended Hubbard model of 1/r2 interaction. This model, defined on a lattice, is part of a large family of integrable one-dimensional multicomponent systems with long range interactions. We study both uniform and nonuniform lattices and present the ground state wavefunctions and energy spectra of these models. In both cases the spectrum is highly degenerate, with the SU (m|n) supersymmetry explaining most of the degeneracies.