Honeycomb Hubbard Model at van Hove Filling Part I: Construction of the Schwinger Functions

This series of two papers is devoted to the rigorous study of the low temperature properties of the two-dimensional weakly interacting Hubbard model on the honeycomb lattice in which the renormalized chemical potential μ has been fixed such that the Fermi surface consists of a set of exact triangles. Using renormalization group analysis around the Fermi surfaces, we prove that this model is not a Fermi liquid, in the mathematically precise sense of Salmhofer. The proof is organized into two parts. In this paper we prove that the perturbation series for Schwinger functions as well as the self-energy function have non-zero radius of convergence when the temperature T is above an exponentially small value, namely T0 ∼ exp (−C|λ|−1/2). In a companion paper [38], we prove the necessary lower bounds for second derivatives of self-energy w.r.t. the external momentum and achieve the proof.