https://doi.org/10.1140/epjb/e2020-10127-1
Regular Article
Friedel oscillations of one-dimensional correlated fermions from perturbation theory and density functional theory
1
Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA – Fundamentals of Future Information Technology,
52056
Aachen, Germany
2
Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich,
52425
Jülich, Germany
3
nanomat/QMAT/CESAM and Department of Physics, Université de Lieg̀e,
4000
Liège, Belgium
a e-mail: jodavic@irb.hr
Received:
10
March
2020
Received in final form:
17
April
2020
Published online: 3 June 2020
We study the asymptotic decay of the Friedel density oscillations induced by an open boundary in a one-dimensional chain of lattice fermions with a short-range two-particle interaction. From Tomonaga-Luttinger liquid theory it is known that the decay follows a power law, with an interaction dependent exponent, which, for repulsive interactions, is larger than the noninteracting value − 1. We first investigate if this behavior can be captured by many-body perturbation theory for either the Green function or the self-energy in lowest order in the two-particle interaction. The analytic results of the former show a logarithmic divergence indicative of the power law. One might hope that the resummation of higher order terms inherent to the Dyson equation then leads to a power law in the perturbation theory for the self-energy. However, the numerical results do not support this. Next we use density functional theory within the local-density approximation and an exchange-correlation functional derived from the exact Bethe ansatz solution of the translational invariant model. While the numerical results are consistent with power-law scaling if systems of 104 or more lattice sites are considered, the extracted exponent is very close to the noninteracting value even for sizeable interactions.
Key words: Solid State and Materials
© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020