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

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.

21 pages, 10 figures

References in corpus (13)

• The density-matrix renormalization group in the age of matrix product states
• The numerical renormalization group method for quantum impurity systems
• "Light-cone" dynamics after quantum quenches in spin chains
• Topological Kondo effect with Majorana fermions
• Real-time simulations of nonequilibrium transport in the single-impurity Anderson model
• Twofold advance in the theoretical understanding of far-from-equilibrium properties of interacting nanostructures
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
• On entropy growth and the hardness of simulating time evolution
• Transport properties and Kondo correlations in nanostructures: the time-dependent DMRG method applied to quantum dots coupled to Wilson chains
• Non-equilibrium electronic transport in a one-dimensional Mott insulator
• Hybrid NRG-DMRG approach to real-time dynamics of quantum impurity systems
• Non-equilibrium transport through a point contact in the $\nu =5/2$ non-Abelian quantum Hall state