Exact diagonalization study of double quantum dots in parallel geometry in zero-bandwidth limit

TL;DR

This paper analytically investigates the quantum states and magnetic correlations in double quantum dots in a zero-bandwidth limit, revealing how tunable parameters influence ferromagnetic and antiferromagnetic behaviors.

Contribution

It provides an exact analytical solution for the eigenstates of double quantum dots in the zero-bandwidth limit, exploring magnetic correlations and phase transitions based on system parameters.

Findings

Identified ground states in different parameter regimes.

Demonstrated transition from ferromagnetic to antiferromagnetic correlation with increasing interdot tunneling.

Showed influence of Coulomb interactions on magnetic correlations and phase behavior.

Abstract

Exact eigenstates of the parallel coupled double quantum dots attached to the non-interacting leads taken in zero-bandwidth limit are analytically obtained in each particle and spin sector. The ground state of the half-filled system is identified from a four dimensional subspace of the twenty dimensional Hilbert space for different values of tunable parameters of the system viz. the energy levels of the quantum dots, the interdot tunneling matrix-element, the ondot and interdot Coulomb interactions and quantities like spin-spin correlation between the dots, occupancies of the dots are calculated. In the parameter space of the interdot tunneling matrix-element and ondot Coulomb interaction, the dots exhibit both ferromagnetic and antiferromagnetic correlation. There is a critical dependency of the interdot tunneling matrix-element on the ondot Coulomb interaction which leads to transition from the ferromagnetic correlation to the antiferromagnetic correlation as the interdot tunneling matrix-element is increased. The ferromagnetic and antiferromagnetic correlations also exist in the absence of interdot tunneling matrix-element through indirect exchange via the leads. The interdot Coulomb interaction is found to affect this dependency considerably.