Transfer-matrix summation of path integrals for transport through nanostructures

TL;DR

This paper introduces TraSPI, a transfer-matrix method based on ISPI, for accurately analyzing nonequilibrium transport in interacting quantum-dot systems with improved efficiency and direct stationary limit implementation.

Contribution

The paper develops a numerically exact transfer-matrix approach, TraSPI, that enhances interpretability and efficiency in studying quantum transport compared to previous ISPI methods.

Findings

TraSPI provides a more transparent formulation of quantum transport.

The method allows direct implementation of the stationary limit.

Application to quantum dots demonstrates its effectiveness.

Abstract

On the basis of the method of iterative summation of path integrals (ISPI), we develop a numerically exact transfer-matrix method to describe the nonequilibrium properties of interacting quantum-dot systems. For this, we map the ISPI scheme to a transfer-matrix approach, which is more accessible to physical interpretation, allows for a more transparent formulation of the theory, and substantially improves the efficiency. In particular, the stationary limit is directly implemented, without the need of extrapolation. The resulting new method, referred to as "transfer-matrix summation of path integrals" (TraSPI), is then applied to resonant electronic transport through a single-level quantum dot.