Hubbard chain with confinement: A model analysis of a finite chain of quantum dots

Ryuichi Ugajin

In a Hubbard chain under an overall confining potential, electrons localized by electron-electron interaction in the center of the chain coexist with electron tunneling through a quasi-Hubbard gap in the center, as suggested by the equal-time Green's function. This mixture of particlelike electrons and wavelike electrons is analyzed using absorption spectra. The effect is expected in a chain of tunneling-coupled nanostructures, e.g., coupled quantum dots.

J. -P. Nikkarila, M. Koskinen, M. Manninen

Guanjie He, Xin Wang

We investigate the entanglement properties in semiconductor quantum dot systems modeled by the extended Hubbard model, focusing on the impacts of potential energy variations and electron interactions within a four-site quantum dot spin chain. Our study explores local and pairwise entanglement across configurations with electron counts N=4 and N=6, under different potential energy settings. By adjusting the potential energy in specific dots and examining the entanglement across various interaction regimes, we identify significant variations in the ground states of quantum dots. We extend this analysis to larger systems with L=6 and L=8, comparing electron counts N=L and N=L+2, revealing sharper entanglement transitions and reduced finite-size effects as the system size increases. Our results show that local potential shifts and the Coulomb interaction strength lead to notable redistributions of the electron configurations in the quantum dot spin chain, significantly affecting the entanglement properties. These changes are depicted in phase diagrams that highlight entanglements' dependencies on the interaction strengths and potential energy adjustments, illustrating complex entanglement dynamics shifts triggered by interdot interactions.

P. B. Jones

Na Young Kim, Tim Byrnes, Kenichiro Kusudo +1 more

Jacob Manalo, Daniel Miravet, Paweł Hawrylak

We present here the steps enabling the microscopic design of a synthetic spin-1 chain in an InAsP quantum dot (QD) array embedded in an InP nanowire. The chain is described by a two-leg multiorbital Hubbard Kanamori (HK) model with parameters obtained from the microscopic calculations of up to eight electrons in a single and double QD. In this HK model describing long arrays of QDs, using both exact diagonalization and matrix product state (MPS) tools, we demonstrate a fourfold quasidegenerate ground state separated from excited states by a finite energy gap similar to a Heisenberg spin-1 chain in the Haldane phase. We demonstrate characteristic behavior of spin-$\frac{1}{2}$ quasiparticles at the edges of the chain by observing the magnetic field dependence of the low-energy spectrum as a function of the applied magnetic field. The applied magnetic field isolates the singlet and ${S}^{z}=0$ triplet states from the other triplet components emulating a singlet-triplet qubit but with macroscopic quantum states. Most importantly, the regions in parameter space where the low-energy spectrum of the multiorbital Hubbard chain yields a Heisenberg spin-1 chain spectrum are mapped out.