The embedding method beyond the single-channel case: Two-mode and Hubbard chains

TL;DR

This paper extends the embedding method to multi-channel systems, specifically two-mode and Hubbard chains, enabling conductance calculations in more complex quantum systems with interactions.

Contribution

The paper introduces a generalized embedding method for multi-channel and Hubbard chains, allowing accurate conductance computation in interacting multi-channel quantum systems.

Findings

Validated the generalized embedding method for Hubbard chains.

Computed conductance for various system sizes and interaction strengths.

Showed how to reduce multi-channel problems to single-channel analyses.

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.