Lindblad equation approach to the optimal working point in nonequilibrium stationary states of an interacting electronic one-dimensional system: Application to the spinless Hubbard chain in the clean and in the weakly disordered limit

TL;DR

This paper uses the Lindblad equation to identify optimal working points in nonequilibrium stationary states of a 1D interacting electronic system, demonstrating robustness against disorder and implications for quantum circuit optimization.

Contribution

It introduces a Lindblad-based method to find optimal working points in a 1D electronic chain, including in the presence of disorder, with applications to quantum circuit tuning.

Findings

Optimal working point identified in the stationary current-bias relationship.

Robustness of the optimal point against localized defects and weak disorder.

Applicability to both interacting and noninteracting spinless fermionic chains.

Abstract

Using the Lindblad equation approach, we derive the range of the parameters of an interacting one-dimensional electronic chain connected to two reservoirs in the large bias limit in which an optimal working point (corresponding to a change in the monotonicity of the stationary current as a function of the applied bias) emerges in the nonequilibrium stationary state. In the specific case of the one-dimensional spinless fermionic Hubbard chain, we prove that an optimal working point emerges in the dependence of the stationary current on the coupling between the chain and the reservoirs, both in the interacting and in the noninteracting case. We show that the optimal working point is robust against localized defects of the chain, as well as against a limited amount of quenched disorder. Eventually, we discuss the importance of our results for optimizing the performance of a quantum circuit by tuning its components as close as possible to their optimal working point.