Laboratoire de Physique Théorique
Toulouse - UMR 5152

We present a framework for organising correlations in strongly interacting quantum systems. First, focusing on the case of interacting electrons, we highlight two ways of representing the electronic degree of freedom, either by the canonical fermion algebra or by the graded Lie algebra su(2|2). The first underlies Landau’s Fermi liquid description of correlated matter, and we identify an alternative Fermi liquid regime governed by the latter. We exploit the su(2|2) algebra to derive a systematic expansion of the electronic correlations, and describe the resulting leading approximation to electronic spectral function. This offers a fresh perspective on the Mott metal-insulator transition. We conclude with a reinterpretation of the meaning of the term ’strongly correlated’, and offer a scheme which encompasses magnetic, electronic, and local moment systems.