Embedding method for the scattering phase in strongly correlated quantum dots

TL;DR

This paper extends the embedding method to compute the full complex transmission amplitude in strongly correlated quantum dot systems, revealing how interactions influence scattering phases and resonant features.

Contribution

The work generalizes the embedding method to obtain the complete scattering matrix at the Fermi energy for interacting quantum dots.

Findings

Interactions narrow resonant peaks without changing zeroes or phase lapses

Scattering phase retains qualitative properties despite strong correlations

Transmission amplitude varies with gate potential in lattice models

Abstract

The embedding method for the calculation of the conductance through interacting systems connected to single channel leads is generalized to obtain the full complex transmission amplitude that completely characterizes the effective scattering matrix of the system at the Fermi energy. We calculate the transmission amplitude as a function of the gate potential for simple diamond-shaped lattice models of quantum dots with nearest neighbor interactions. In our simple models we do not generally observe an interaction dependent change in the number of zeroes or phase lapses that depend only on the symmetry properties of the underlying lattice. Strong correlations separate and reduce the widths of the resonant peaks while preserving the qualitative properites of the scattering phase.