Eur. Phys. J. B 75, 253-266 (2010)
https://doi.org/10.1140/epjb/e2010-00153-y

The embedding method beyond the single-channel case

Two-mode and Hubbard chains

¹ Service de Physique de l'État Condensé (CNRS URA 2464), IRAMIS/SPEC, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
² Institut Néel, 25 avenue des Martyrs, BP 166, 38042 Grenoble Cedex 9, France
³ Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 (UdS-CNRS), 23 rue du Loess, BP 43, 67034 Strasbourg Cedex 2, France
⁴ Institut für Nanotechnologie, Karlsruher Institut für Technologie, 76344 Eggenstein-Leopoldshafen, Germany
⁵ Institut für Physik, Universität Augsburg, Universitätsstraße 1, 86135 Augsburg, Germany

Corresponding author: Dietmar.Weinmann@ipcms.u-strasbg.fr

Received: 25 September 2009
Revised: 26 February 2010
Published online: 19 May 2010

Abstract

We investigate the relationship between persistent currents in multi-channel rings containing an embedded scatterer and the conductance through the same scatterer attached to leads. The case of two uncoupled channels corresponds to a Hubbard chain, for which the one-dimensional embedding method is readily generalized. Various tests are carried out to validate this new procedure, and the conductance of short one-dimensional Hubbard chains attached to perfect leads is computed for different system sizes and interaction strengths. In the case of two coupled channels the conductance can be obtained from a statistical analysis of the persistent current or by reducing the multi-channel scattering problem to several single-channel setups.