Matrix product state simulations of quantum quenches and transport in Coulomb blockaded superconducting devices

TL;DR

This paper introduces a matrix product state method to simulate real-time transport in Coulomb blockaded superconducting devices, capturing non-perturbative effects like Coulomb diamonds and Majorana-induced zero-bias peaks.

Contribution

The authors develop a novel MPS-based approach combining Wilson chains and mean-field BCS theory to efficiently simulate quantum quenches in superconducting devices with Coulomb blockade.

Findings

Successfully reproduces Coulomb diamond structures with subgap states.

Captures sequential tunneling and cotunneling phenomena.

Analyzes Majorana zero-bias peaks and compares with Breit-Wigner predictions.

Abstract

Superconducting devices subject to strong charging energy interactions and Coulomb blockade are one of the key elements for the development of nanoelectronics and constitute common building blocks of quantum computation platforms and topological superconducting setups. The study of their transport properties is non-trivial and some of their non-perturbative aspects are hard to capture with the most ordinary techniques. Here we present a matrix product state approach to simulate the real-time dynamics of these systems. We propose a study of their transport based on the analysis of the currents after quantum quenches connecting such devices with external leads. Our method is based on the combination of a Wilson chain construction for the leads and a mean-field BCS description for the superconducting scatterers. In particular, we employ a quasiparticle energy eigenbasis which greatly reduces their entanglement growth and we introduce an auxiliary degree of freedom to encode the device total charge. This approach allows us to treat non-perturbatively both their charging energy and coupling with external electrodes. We show that our construction is able to describe the Coulomb diamond structure of a superconducting dot with subgap states, including its sequential tunneling and cotunneling features. We also study the conductance zero-bias peaks caused by Majorana modes in a blockaded Kitaev chain, and compare our results with common Breit-Wigner predictions.