A rigorous treatment of the perturbation theory for many-electron systems

Abstract

Four point correlation functions for many electrons at finite temperature in periodic lattice are analyzed by the perturbation theory with respect to the coupling constant. The correlation functions are characterized as a limit of finite dimensional Grassmann integrals. A lower bound on the radius of convergence and an upper bound on the perturbation series are obtained. The perturbation series up to second order is numerically implemented along with the volume-independent upper bounds on the sum of the higher order terms in 2 dimensional case.

61 pages

References in corpus (5)

• Decay of Superconducting and Magnetic Correlations in One- and Two-Dimensional Hubbard Models
• Determinant Bounds and the Matsubara UV Problem of Many-Fermion Systems
• Positivity and Convergence in Fermionic Quantum Field Theory
• Clustering of fermionic truncated expectation values via functional integration
• Renormalization of the 2-point function of the Hubbard model at half-filling

Cited by in corpus (2)

• The algebra of Grassmann canonical anti-commutation relations (GAR) and its applications to fermionic systems
• Exponential decay of correlation functions in many-electron systems