Authors: Giuseppe Benfatto, Pierluigi Falco, Vieri Mastropietro

Title: Universality of one-dimensional Fermi systems, I. Response functions and critical exponents
 
Abstract: The critical behavior of one-dimensional interacting Fermi systems is expected to display universality features, called Luttinger liquid behavior. Critical exponents and certain thermodynamic quantities are expected to be related among each others by model-independent formulas. We establish such relations, the proof of which has represented a challenging mathematical problem, for a general model of spinning fermions on a one dimensional lattice; interactions are short ranged and satisfy a positivity condition which makes the model critical at zero temperature. Proofs are reported in two papers: in the present one, we demonstrate that the zero temperature response functions in the thermodynamic limit are Borel summable and have anomalous power-law decay with multiplicative logarithmic corrections. Critical exponents are expressed in terms of convergent expansions and depend on all the model details. All results are valid for the special case of the Hubbard model.

Keywords: 1D Hubbard model, Luttinger liquid behavior, critical exponents, renormalization group

Giuseppe Benfatto
Dipartimento di Matematica
Università di Roma Tor Vergata
V.le della Ricerca Scientifica 1, 00133 Roma - Italy
e-mail: benfatto AT mat DOT uniroma2 DOT it

Pierluigi Falco
Department of Mathematics
California State University, Northridge
e-mail: pierluigi DOT falco AT csun DOT edu

Vieri Mastropietro
Dipartimento di Matematica
Università di Milano
Via Saldini, 50, I-20133 Milano - ITALY
e-mail: Vieri DOT Mastropietro AT unimi DOT it