KTH/Nordita/SU seminar in Theoretical Physics

Luttinger and Fermi liquids: a Constructive Renormalization Group approach

by Vieri Mastropietro (Università di Roma "Tor Vergata")



The anomalous properties of high Tc superconductors have led to a quest for a better understanding of interacting fermions, beyond the assumptions and approximations usually done. The methods of Constructive Quantum Field Theory allow the non-perturbative investigation of such systems, proving the convergence of the series involved. Non Fermi liquid behavior (like Luttinger or more complex behavior) has been rigorously established in several models, not treatable by bosonization, like the 1d Hubbard model, the XYZ chain, the Askhin-Teller model and so on. On the contrary, Fermi liquid behavior has been proved in the 2D Hubbard model away from half-filling and above exponentially small temperatures. If the Fermi surface has flat pieces, for certain special interactions Luttinger liquid behavior is found.