{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:13:36Z","timestamp":1760058816018,"version":"build-2065373602"},"reference-count":78,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T00:00:00Z","timestamp":1745884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12474489","CityU 11304920","JCYJ20240813153139050","GDZX2203001","GDZX2403001","2021ZD0302300"],"award-info":[{"award-number":["12474489","CityU 11304920","JCYJ20240813153139050","GDZX2203001","GDZX2403001","2021ZD0302300"]}]},{"name":"Research Grants Council of Hong Kong","award":["12474489","CityU 11304920","JCYJ20240813153139050","GDZX2203001","GDZX2403001","2021ZD0302300"],"award-info":[{"award-number":["12474489","CityU 11304920","JCYJ20240813153139050","GDZX2203001","GDZX2403001","2021ZD0302300"]}]},{"name":"Shenzhen Fundamental Research Program","award":["12474489","CityU 11304920","JCYJ20240813153139050","GDZX2203001","GDZX2403001","2021ZD0302300"],"award-info":[{"award-number":["12474489","CityU 11304920","JCYJ20240813153139050","GDZX2203001","GDZX2403001","2021ZD0302300"]}]},{"name":"Guangdong Provincial Quantum Science Strategic Initiative","award":["12474489","CityU 11304920","JCYJ20240813153139050","GDZX2203001","GDZX2403001","2021ZD0302300"],"award-info":[{"award-number":["12474489","CityU 11304920","JCYJ20240813153139050","GDZX2203001","GDZX2403001","2021ZD0302300"]}]},{"name":"Innovation Program for Quantum Science and Technology","award":["12474489","CityU 11304920","JCYJ20240813153139050","GDZX2203001","GDZX2403001","2021ZD0302300"],"award-info":[{"award-number":["12474489","CityU 11304920","JCYJ20240813153139050","GDZX2203001","GDZX2403001","2021ZD0302300"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2019 dependencies on the interaction strengths and potential energy adjustments, illustrating complex entanglement dynamics shifts triggered by interdot interactions.<\/jats:p>","DOI":"10.3390\/e27050479","type":"journal-article","created":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T09:00:39Z","timestamp":1745917239000},"page":"479","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Exploring Entanglement Spectra and Phase Diagrams in Multi-Electron Quantum Dot Chains"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9739-3215","authenticated-orcid":false,"given":"Guanjie","family":"He","sequence":"first","affiliation":[{"name":"Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2971-5088","authenticated-orcid":false,"given":"Xin","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR, China"},{"name":"Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China"},{"name":"Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen 518045, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1103\/RevModPhys.77.513","article-title":"Quantum information with continuous variables","volume":"77","author":"Braunstein","year":"2005","journal-title":"Rev. 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