Luttinger and Fermi liquids: a Constructive Renormalization Group
(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
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.