High-precision real-space simulation of electrostatically-confined few-electron states

Abstract

In this paper we present a computational procedure that utilizes real-space grids to obtain high precision approximations of electrostatically confined few-electron states such as those that arise in gated semiconductor quantum dots. We use the Full Configuration Interaction (FCI) method with a continuously adapted orthonormal orbital basis to approximate the ground and excited states of such systems. We also introduce a benchmark problem based on a realistic analytical electrostatic potential for quantum dot devices. We show that our approach leads to highly precise computed energies and energy differences over a wide range of model parameters. The analytic definition of the benchmark allows for a collection of tests that are easily replicated, thus facilitating comparisons with other computational approaches.

Semiconductor spin qubits

“…In the FCI approach, first developed for quantum chemistry (Szabo and Ostlund, 1996), a set of 2K singleparticle spin orbital basis states {φ m (r)χ σ } is chosen which are product states of real-space basis functions and spinors; the former may be convenient analytic functions or eigenstates of the single-particle operator T in Eq. ( 17) (Anderson et al, 2022;Joecker et al, 2021;Rontani, 2006). Often, K ≈ 20 − 40 orbitals are needed to obtain fully converged dot or donor states.…”