A Novel Approach to Study Highly Correlated Nanostructures: The Logarithmic Discretization Embedded Cluster Approximation

TL;DR

The paper introduces LDECA, a new method combining cluster diagonalization and logarithmic discretization, to analyze transport in highly correlated nanostructures, validated against known solutions and applicable to complex quantum systems.

Contribution

LDECA is a novel approach that integrates cluster diagonalization with Wilson's logarithmic discretization for studying correlated nanostructures.

Findings

LDECA results agree with Bethe ansatz for single-dot systems.

LDECA captures two-stage Kondo physics in double-dot systems.

Method is suitable for complex molecular and quantum dot transport problems.

Abstract

This work proposes a new approach to study transport properties of highly correlated local structures. The method, dubbed the Logarithmic Discretization Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite cluster containing the many-body terms of the Hamiltonian and embedding it into the rest of the system, combined with Wilson's idea of a logarithmic discretization of the representation of the Hamiltonian. The physics associated with both one embedded dot and a double-dot side-coupled to leads is discussed in detail. In the former case, the results perfectly agree with Bethe ansatz data, while in the latter, the physics obtained is framed in the conceptual background of a two-stage Kondo problem. A many-body formalism provides a solid theoretical foundation to the method. We argue that LDECA is well suited to study complicated problems such as transport through molecules or quantum dot structures with complex ground states.