One-Dimensional Hubbard Model in High Temperatures Through Many-Body Perturbation Theory

M.A. Taga, A. Hafdallahb aComputational Physics and Quantum Phenomena Laboratory (CPQPL), Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria bLPAT Laboratory, Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria

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We present symbolic algorithms designed to investigate the perturbative expansions of the d-Hubbard model. These methods are part of recent developments in many-body perturbation theory that aim to reformulate Feynman diagrams in terms of divided differences. The direct application of this technique to the one-dimensional Hubbard model yields the coefficients of the grand potential up to the sixth order, expressed in terms of both the interacting potential (U expansions) and high-temperature expansions (β expansions). A key feature of this approach is the ability to merge the β expansions to any desired order. To verify our analytical results, we compare the derived magnetic susceptibility with the exact solution of the quantum transfer matrix method in the half-filled case.

DOI:10.12693/APhysPolA.147.79 topics: divided differences, many-body perturbation theory (MBPT), Feynman vacuum diagrams, finite temperature