Exclusion statistics and strongly correlated electron systems

Abstract

We generalize Haldane's definition of exclusion statistics to systems with infinite dimensional Hilbert spaces. We then show that the statistics parameter is completely determined by the high temperature limit of the second virial coefficient, when the virial expansion exists in this limit. Next we address the question as to when quasiparticles with nontrivial exclusion statistics can occur in interacting electron systems and argue that they would occur in systems where Fermi liquid theory breaks down. We then discuss some explicit examples in one dimensional systems where this is known to happen. From these we abstract general constraints on the occupation numbers for exclusion anyons. Finally we give examples of some physical systems, spin chains and impurity problems, where the phenomenon is predicted to occur.