Broken symmetry solutions in one-dimensional lattice models via many-body perturbation theory
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arXiv
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| Format: | Preprint |
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2024
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| author | Quinzi, Matteo Chiarotti, Tommaso Gibertini, Marco Ferretti, Andrea |
| author_facet | Quinzi, Matteo Chiarotti, Tommaso Gibertini, Marco Ferretti, Andrea |
| contents | In this work we study self-consistent solutions in one-dimensional lattice models obtained via many-body perturbation theory. The Dyson equation is solved in a fully self-consistent manner via the algorithmic-inversion method based on the sum-over-poles representation (AIM-SOP) of dynamical operators. In particular, we focus on the GW approximation, analyzing the spectral properties and the emergence of possible magnetic- or charge-density-wave broken symmetry solutions. We start by validating our self-consistent AIM-SOP implementation by taking as test case the one-dimensional Hubbard model. We then move to the study of antiferromagnetic and charge density wave solutions in one-dimensional lattice models, taking into account a long-range Coulomb interaction between the electrons. We show that moving from local to non-local electronic interactions leads to a competition between antiferromagnetic and charge-density-wave broken symmetry solutions. Complementary, by solving the Sham-Schlüter equation, we can compute the non-interacting Green's function reproducing the same charge density of the interacting system. In turn, this allows for the evaluation of the derivative discontinuity of the Kohn-Sham (KS) potential, showing that its contribution to the fundamental gap can become dominating in some of the studied cases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_15020 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Broken symmetry solutions in one-dimensional lattice models via many-body perturbation theory Quinzi, Matteo Chiarotti, Tommaso Gibertini, Marco Ferretti, Andrea Strongly Correlated Electrons Materials Science In this work we study self-consistent solutions in one-dimensional lattice models obtained via many-body perturbation theory. The Dyson equation is solved in a fully self-consistent manner via the algorithmic-inversion method based on the sum-over-poles representation (AIM-SOP) of dynamical operators. In particular, we focus on the GW approximation, analyzing the spectral properties and the emergence of possible magnetic- or charge-density-wave broken symmetry solutions. We start by validating our self-consistent AIM-SOP implementation by taking as test case the one-dimensional Hubbard model. We then move to the study of antiferromagnetic and charge density wave solutions in one-dimensional lattice models, taking into account a long-range Coulomb interaction between the electrons. We show that moving from local to non-local electronic interactions leads to a competition between antiferromagnetic and charge-density-wave broken symmetry solutions. Complementary, by solving the Sham-Schlüter equation, we can compute the non-interacting Green's function reproducing the same charge density of the interacting system. In turn, this allows for the evaluation of the derivative discontinuity of the Kohn-Sham (KS) potential, showing that its contribution to the fundamental gap can become dominating in some of the studied cases. |
| title | Broken symmetry solutions in one-dimensional lattice models via many-body perturbation theory |
| topic | Strongly Correlated Electrons Materials Science |
| url | https://arxiv.org/abs/2412.15020 |