{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T00:35:31Z","timestamp":1760574931467,"version":"build-2065373602"},"reference-count":66,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T00:00:00Z","timestamp":1760486400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12074431","12374252","12274384"],"award-info":[{"award-number":["12074431","12374252","12274384"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Innovation Program of Hunan Province","award":["2024RC1046"],"award-info":[{"award-number":["2024RC1046"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12404332"],"award-info":[{"award-number":["12404332"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum spin transport in integrable systems reveals a rich nonequilibrium phenomena that challenges the conventional hydrodynamic framework. Recent advances in ultracold atom experiments with state preparation and single-site addressing have enabled the understanding of this anomalous behavior. Particularly, the full universality characterization of exotic initial states, as well as their measurement representation, remain unknown. By employing tensor network and contrast methods, we systematically investigate spin transport in the quantum XXZ spin chain and extract dynamical scaling exponents emerging from two paradigmatic and experimentally attainable initial states, i.e., multi-periodic domain-wall (MPDW) and spin-helix (SH) states. Our results using different values of anisotropic parameters \u0394\u2208[0,1.2] demonstrate the evident impeded transport and the difference between the two states with increasing \u0394 values. Large-scale and consistent simulations confirm the contrast method as a viable scaling extraction approach for exotic states with periodicity within experimentally accessible timescales. Our work establishes a foundation for studying initial memory and the corresponding relations of emergent transport behavior in nonequilibrium quantum systems, opening avenues for the identification of their unique universality classes.<\/jats:p>","DOI":"10.3390\/e27101070","type":"journal-article","created":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T10:12:29Z","timestamp":1760523149000},"page":"1070","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Contrast Analysis on Spin Transport of Multi-Periodic Exotic States in the XXZ Chain"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-4707-8298","authenticated-orcid":false,"given":"Shixian","family":"Jiang","sequence":"first","affiliation":[{"name":"College of Science, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Jianpeng","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Science, National University of Defense Technology, Changsha 410073, China"},{"name":"Hunan Key Laboratory of Extreme Matter and Applications, National University of Defense Technology, Changsha 410073, China"},{"name":"Hunan Research Center of the Basic Discipline for Physical States, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Yongqiang","family":"Li","sequence":"additional","affiliation":[{"name":"College of Science, National University of Defense Technology, Changsha 410073, China"},{"name":"Hunan Key Laboratory of Extreme Matter and Applications, National University of Defense Technology, Changsha 410073, China"},{"name":"Hunan Research Center of the Basic Discipline for Physical States, National University of Defense Technology, Changsha 410073, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"045006","DOI":"10.1103\/RevModPhys.94.045006","article-title":"Nonequilibrium boundary-driven quantum systems: Models, methods, and properties","volume":"94","author":"Landi","year":"2022","journal-title":"Rev. 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