# Long-range Entanglement of Kondo Clouds in Open Triple Quantum Dots

## TL;DR

This paper investigates the long-range entanglement of Kondo clouds in an open triple quantum dot system using DEOM theory, revealing how spectral features and correlations indicate overlapping Kondo clouds and their dependence on temperature and coupling.

## Contribution

It provides a detailed analysis of Kondo cloud entanglement in OTQDs, highlighting the spectral and correlation signatures of overlapping Kondo clouds in this system.

## Key findings

- Spectral peak in intermediate QD indicating overlapping Kondo clouds
- Negative spin-spin correlations between adjacent and peripheral QDs
- Enhanced Kondo cloud entanglement with decreasing temperature and increasing dot-lead coupling

## Abstract

We study entanglement of Kondo clouds in an open triple quantum dots (OTQDs) system based on the dissipaton equation of motion (DEOM) theory. A comprehensive picture of the long-range entanglement of Kondo clouds is sketched by the spectral functions, spin-spin correlation and dot occupancies of OTQDs. We find that for the configuration (N1,N2,N3) = (1, 0, 1), a conduction electrons peak occurs in the spectral function of intermediate QD in Kondo regime. This peak resulting from the overlapping of the two Kondo clouds forming from between the two peripheral QDs and leads, enhances with decreasing temperature and increasing dot-lead coupling. Both the spin-spin correlations between the two adjacent QDs and the two peripheral QDs owns negative values. It also confirms the physical picuture of the overlapping between left and right Kondo clouds via the intermediate QD. Moreover, the transition of the effective electron occupation and the spectral function of intermediate QD in Kondo regime also indicates the entanglement of Kondo clouds enhancing with decreasing temperature and increasing dot-lead coupling. This investigation will be beneficial to detect the Kondo clouds and to further explore Kondo physics in related experiment setups.