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

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Published: Feb 27, 2025
DOI: https://doi.org/10.12693/APhysPolA.147.79
Keywords:
divided differences, many-body perturbation theory (MBPT), Feynman vacuum diagrams, finite temperature

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M.A. Tag
Computational Physics and Quantum Phenomena Laboratory (CPQPL), Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria
A. Hafdallah
LPAT Laboratory, Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria

Abstract

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.

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How to Cite
[1]
M. Tag and A. Hafdallah, “One-Dimensional Hubbard Model in High Temperatures Through Many-Body Perturbation Theory”, Acta Phys. Pol. A, vol. 147, no. 2, p. 79, Feb. 2025, doi: 10.12693/APhysPolA.147.79.
Issue
Vol. 147 No. 2 (2025): Acta Physica Polonica A
Section
Regular segment
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This work is licensed under a Creative Commons Attribution 4.0 International License.

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M.A. Tag, High Temperature Series Expansion of 1D Hubbard Model, 2025