Spatial entanglement of fermions in one-dimensional quantum dots

TL;DR

This paper introduces a quantum Monte Carlo method to analyze spatial entanglement of electrons in one-dimensional quantum dots, revealing how spin configurations influence entanglement and correlating results with exact calculations.

Contribution

The paper presents a novel time-dependent quantum Monte Carlo approach for fermions to quantify spatial entanglement in quantum dots with various spin states.

Findings

Spatial entanglement is small in parallel-spin configurations.

Opposite-spin electrons in spin-compensated cases behave like bosons, increasing entanglement.

Results closely match numerically exact calculations.

Abstract

The time dependent quantum Monte Carlo method for fermions is introduced and applied for calculation of entanglement of electrons in one-dimensional quantum dots with several spin-polarized and spin-compensated electron configurations. The rich statistics of wave functions provided by the method allows one to build reduced density matrices for each electron and to quantify the spatial entanglement using measures such as quantum entropy by treating the electrons as identical or distinguishable particles. Our results indicate that the spatial entanglement in parallel-spin configurations is rather small and it is determined mostly by the quantum nonlocality introduced by the ground state. By contrast, in the spin-compensated case the outermost opposite-spin electrons interact like bosons which prevails their entanglement, while the inner shell electrons remain largely at their Hartree-Fock geometry. Our findings are in a close correspondence with the numerically exact results, wherever such comparison is possible.