Renormalization group analysis of multi-band many-electron systems at half-filling (Q2804480)

One proposes an approach via renormalization to the analysis of multi-band many-electron systems at positive temperature. The purpose of this long paper is two-fold. Firstly one constructs necessary estimates for the multi-scale integrations on a finite-dimensional Grassmann algebra, and next, one applies the general estimates so obtained to a special many-electron model in order to obtain some results for low temperatures. The paper is organized as follows. Definition of the Hamiltonian operator so referred to; derivation of norm estimates on single-scale integrations; derivation of norm estimates on the difference between single-scale integrations for two different temperatures; application to the construction of ultra-violet (UV) integration process and infrared integration (IR) process; relation with Matsubara frequency; and lastly applications of the estimation previously obtained to Hamiltonian model to derive the main result. The proof of the latter is based on a four-band formulation of the Hamiltonian model and an extension of the renormalization technique designed for the half-filled Hubbard model on the honeycomb lattice.