On the Scaling Limit of the 1D Hubbard Model at Half Filling

TL;DR

This paper investigates the scaling limit of the 1D Hubbard model at half filling, deriving its dispersion relations and S-matrix, and identifying its scattering theory as an SU(2) chiral-invariant Thirring field theory with both massive and massless sectors.

Contribution

It provides a detailed analysis of the Hubbard model's scaling limit and establishes its connection to a known integrable quantum field theory.

Findings

Derived a small-coupling expansion of lattice dispersion relations.

Identified the scattering theory as SU(2) chiral-invariant Thirring model.

Connected the Hubbard model to a well-understood field theory.

Abstract

The dispersion relations and S-matrix of the one-dimensional Hubbard model at half filling are considered in a certain scaling limit. (In the process we derive a useful small-coupling expansion of the exact lattice dispersion relations.) The resulting scattering theory is consistently identified as that of the SU(2) chiral-invariant Thirring (or Gross-Neveu) field theory, containing both massive and massless sectors.