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arXiv · 2412.15020

Broken symmetry solutions in one-dimensional lattice models via many-body perturbation theory

Matteo Quinzi·Tommaso Chiarotti·Marco Gibertini·Andrea Ferretti
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Abstract

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-Schl\"uter 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.

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Matteo Quinzi, Tommaso Chiarotti, Marco Gibertini, Andrea Ferretti. 2024-12-19. Broken symmetry solutions in one-dimensional lattice models via many-body perturbation theory. https://doi.org/10.1103/physrevb.111.125148

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