FM 04-2013 (arXiv:1303.3684)

Authors: Giuseppe Benfatto, Pierluigi Falco, Vieri Mastropietro

Title: Universality of one-dimensional Fermi systems, II. The Luttinger liquid structure
Abstract: The critical behavior of one-dimensional interacting Fermi systems is expected to display universality features. For example, critical exponents and certain thermodynamic quantities, even though dependent on microscopic parameters of the model, are expected to be related among each others by model-independent formulas. So far, universality theory predictions have been partially veried in some of those models for which an exact solution is known; however, in the general case, exact solutions are not available, and the validity of the theory has represented a challenging mathematical problem. We establish universality formulas 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. For such model at generic value of the parameters, an exact solution is not known. Proofs are reported in two papers: in the previous paper we showed that the zero temperature response functions have anomalous power-law decay with multiplicative logarithmic corrections; in the present paper we make use of the Ward Identities due to asymptotically emerging symmetries to establish the universal relations predicted on the basis of the Luttinger liquid conjecture.

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

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