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

TL;DR

This paper develops a self-consistent many-body perturbation theory approach using the AIM-SOP algorithm to study symmetry-breaking solutions in one-dimensional lattice models, revealing the interplay of magnetic and charge orderings.

Contribution

It introduces a fully self-consistent AIM-SOP method for solving the Dyson equation in lattice models, analyzing symmetry-breaking phenomena with long-range interactions.

Findings

Validated the AIM-SOP implementation on the 1D Hubbard model.

Identified competition between antiferromagnetic and charge-density-wave solutions.

Showed the importance of the Kohn-Sham potential's derivative discontinuity in gap calculations.

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.