{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:10:22Z","timestamp":1760058622161,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,12]],"date-time":"2025-04-12T00:00:00Z","timestamp":1744416000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Stavros Niarchos Foundation (SNF) and the Hellenic Foundation for Research and Innovation (H.F.R.I.)","award":["011496","896626"],"award-info":[{"award-number":["011496","896626"]}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["011496","896626"],"award-info":[{"award-number":["011496","896626"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Linear tight-binding models with long-range interactions and small-world geometry have a broad energy spectrum in the nearest neighbor coupling limit, while the spectrum becomes narrow in the fully connected limit due to the emergence of flat bands. A transition to a Wigner-like density of states appears at a low fraction of long-range bonds. Adding nonlinearity to the model introduces correlations among the stationary states, while multiple new states are generated as a result of the nonlinearity. In this work, we study the effect of band correlations on the local density of states for small-world networks as a function of the number of long-range bonds. We find that close to the nearest neighbor limit, the onset of correlations shifts the nonlinear density of states towards the band edge of the spectrum. Close to the opposite limit of the fully connected model, the band collapses in the band center, accompanied by a large increase in the new states induced by the nonlinearity. While in both limits the effect of correlations is to flatten the band, close to the mean field fully connected limit, the states are correlated and generally have distinct localized features. These effects may have implications for the dynamics of electrons in two-dimensional moir\u00e9 structures and the onset of superconductivity in these systems.<\/jats:p>","DOI":"10.3390\/e27040420","type":"journal-article","created":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T06:18:36Z","timestamp":1744611516000},"page":"420","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Statistical Properties of Correlated Semiclassical Bands in Tight-Binding Small-World Networks"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0499-7691","authenticated-orcid":false,"given":"Natalya","family":"Almazova","sequence":"first","affiliation":[{"name":"Institute of Theoretical and Computational Physics, Department of Physics, University of Crete, 71003 Heraklion, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4793-0224","authenticated-orcid":false,"given":"Giorgos P.","family":"Tsironis","sequence":"additional","affiliation":[{"name":"Institute of Theoretical and Computational Physics, Department of Physics, University of Crete, 71003 Heraklion, Greece"},{"name":"John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4682-0165","authenticated-orcid":false,"given":"Efthimios","family":"Kaxiras","sequence":"additional","affiliation":[{"name":"John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA"},{"name":"Department of Physics, Harvard University, Cambridge, MA 02138, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1038\/nature26154","article-title":"Correlated insulator behaviour at half-filling in magic-angle graphene superlattices","volume":"556","author":"Cao","year":"2018","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1038\/nature26160","article-title":"Unconventional superconductivity in magic-angle graphene superlattices","volume":"556","author":"Cao","year":"2018","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"12233","DOI":"10.1073\/pnas.1108174108","article-title":"Moir\u00e9 bands in twisted double-layer graphene","volume":"108","author":"Bistritzer","year":"2011","journal-title":"Proc. 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