Pairwise entanglement and the Mott transition for correlated electrons in nanochains

TL;DR

This paper investigates how pairwise entanglement in charge and spin degrees of freedom can serve as a signature of the Mott transition in correlated nanoscopic systems, using exact diagonalization methods.

Contribution

It introduces a novel entanglement-based approach to identify the Mott transition in nanochains, with explicit formulas linking concurrence to ground-state correlations.

Findings

Charge concurrence vanishes at the Mott transition.

Spin concurrence remains nonzero in the insulating phase.

Charge and spin degrees of freedom can decouple in entangled states.

Abstract

Pairwise entanglement, calculated separately for charge and spin degrees of freedom, is proposed as a ground-state signature of the Mott transition in correlated nanoscopic systems. Utilizing the exact diagonalization - ab initio method (EDABI), for chains containing $N\leqslant{}16$ hydrogenic-like atoms (at the half filling), we find that the vanishing of the nearest-neighbor charge concurrence indicates the crossover from a partly-localized quantum liquid to the Mott insulator. Spin concurrence remains nonzero at the insulating phase, showing that the decopling of spin and charge degrees of freedom may manifest itself by wavefunctions entangled in spin, but separable in charge coordinates. At the quarter filling, the analysis for $N\leqslant{}20$ shows that spin concurrence vanishes immediately when the charge-energy gap obtained from the scaling with $1/N\rightarrow{}0$ vanishes, constituting a finite-system version of the Mott transition. Analytic derivations of the formulas expressing either charge or spin concurrence in terms of ground-state correlation functions are also provided.