{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T14:56:05Z","timestamp":1767970565775,"version":"3.49.0"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:00:00Z","timestamp":1761609600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:00:00Z","timestamp":1761609600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s10444-025-10266-4","type":"journal-article","created":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T07:52:12Z","timestamp":1761637932000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A highly accurate procedure for computing globally optimal Wannier functions in one-dimensional crystalline insulators"],"prefix":"10.1007","volume":"51","author":[{"given":"Abinand","family":"Gopal","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6678-6278","authenticated-orcid":false,"given":"Hanwen","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,10,28]]},"reference":[{"key":"10266_CR1","doi-asserted-by":"crossref","unstructured":"Bj\u00f6rck, \u00c5.: Numerical Methods in Matrix Computations, vol.\u00a059. Springer (2015)","DOI":"10.1007\/978-3-319-05089-8"},{"key":"10266_CR2","doi-asserted-by":"crossref","unstructured":"Blount, E.I.: Formalisms of band theory. In: Solid State Physics, vol.\u00a013, pp. 305\u2013373. Elsevier (1962)","DOI":"10.1016\/S0081-1947(08)60459-2"},{"key":"10266_CR3","unstructured":"Boyd, J.P.: Chebyshev and Fourier Spectral Methods. Courier Corporation (2001)"},{"issue":"7","key":"10266_CR4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.95.075114","volume":"95","author":"\u00c9 Canc\u00e8s","year":"2017","unstructured":"Canc\u00e8s, \u00c9., Levitt, A., Panati, G., Stoltz, G.: Robust determination of maximally localized Wannier functions. Phys. Rev. B 95(7), 075114 (2017)","journal-title":"Phys. Rev. B"},{"key":"10266_CR5","doi-asserted-by":"crossref","unstructured":"Cornean, H.D., Herbst, I., Nenciu, G.: On the construction of composite Wannier functions. In: Annales Henri Poincar\u00e9, vol.\u00a017, pp. 3361\u20133398. Springer (2016)","DOI":"10.1007\/s00023-016-0489-2"},{"issue":"1","key":"10266_CR6","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1137\/18M1167164","volume":"17","author":"A Damle","year":"2019","unstructured":"Damle, A., Levitt, A., Lin, L.: Variational formulation for Wannier functions with entangled band structure. Multiscale Model. Simul. 17(1), 167\u2013191 (2019)","journal-title":"Multiscale Model. Simul."},{"issue":"3","key":"10266_CR7","doi-asserted-by":"publisher","first-page":"1392","DOI":"10.1137\/17M1129696","volume":"16","author":"A Damle","year":"2018","unstructured":"Damle, A., Lin, L.: Disentanglement via entanglement: a unified method for Wannier localization. Multiscale Model. Simul. 16(3), 1392\u20131410 (2018)","journal-title":"Multiscale Model. Simul."},{"key":"10266_CR8","unstructured":"Deimling, K.: Ordinary Differential Equations in Banach Spaces, vol. 596. Springer (2006)"},{"issue":"3A","key":"10266_CR9","doi-asserted-by":"publisher","first-page":"A698","DOI":"10.1103\/PhysRev.135.A698","volume":"135","author":"J Des Cloizeaux","year":"1964","unstructured":"Des Cloizeaux, J.: Analytical properties of $$n$$-dimensional energy bands and Wannier functions. Phys. Rev. 135(3A), A698 (1964)","journal-title":"Phys. Rev."},{"key":"10266_CR10","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1023\/A:1022338906936","volume":"40","author":"A Dutt","year":"2000","unstructured":"Dutt, A., Greengard, L., Rokhlin, V.: Spectral deferred correction methods for ordinary differential equations. BIT Numer. Math. 40, 241\u2013266 (2000)","journal-title":"BIT Numer. Math."},{"key":"10266_CR11","unstructured":"Golub, G.H., Van\u00a0Loan, C.F.: Matrix Computations. Johns Hopkins University Press, 4 edition (2013)"},{"issue":"3","key":"10266_CR12","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1137\/S003614450343200X","volume":"46","author":"L Greengard","year":"2004","unstructured":"Greengard, L., Lee, J.-Y.: Accelerating the nonuniform fast Fourier transform. SIAM Rev. 46(3), 443\u2013454 (2004)","journal-title":"SIAM Rev."},{"key":"10266_CR13","unstructured":"Kato, T.: Perturbation Theory for Linear Operators, vol. 132. Springer Science & Business Media (1980)"},{"issue":"4","key":"10266_CR14","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1103\/PhysRev.115.809","volume":"115","author":"W Kohn","year":"1959","unstructured":"Kohn, W.: Analytic properties of Bloch waves and Wannier functions. Phys. Rev. 115(4), 809 (1959)","journal-title":"Phys. Rev."},{"issue":"4","key":"10266_CR15","doi-asserted-by":"publisher","first-page":"1419","DOI":"10.1103\/RevModPhys.84.1419","volume":"84","author":"N Marzari","year":"2012","unstructured":"Marzari, N., Mostofi, A.A., Yates, J.R., Souza, I., Vanderbilt, D.: Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84(4), 1419\u20131475 (2012)","journal-title":"Rev. Mod. Phys."},{"issue":"20","key":"10266_CR16","doi-asserted-by":"publisher","first-page":"12847","DOI":"10.1103\/PhysRevB.56.12847","volume":"56","author":"N Marzari","year":"1997","unstructured":"Marzari, N., Vanderbilt, D.: Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56(20), 12847 (1997)","journal-title":"Phys. Rev. B"},{"key":"10266_CR17","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1007\/s002200050251","volume":"190","author":"A Nenciu","year":"1998","unstructured":"Nenciu, A., Nenciu, G.: The existence of generalised Wannier functions for one-dimensional systems. Commun. Math. Phys. 190, 541\u2013548 (1998)","journal-title":"Commun. Math. Phys."},{"issue":"16","key":"10266_CR18","first-page":"165902","volume":"32","author":"G Pizzi","year":"2020","unstructured":"Pizzi, G., Vitale, V., Arita, R., Bl\u00fcgel, S., Freimuth, F., G\u00e9ranton, G., Gibertini, M., Gresch, D., Johnson, C., Koretsune, T., et al.: Wannier90 as a community code: New features and applications. J. Phys.: Condens. Matter 32(16), 165902 (2020)","journal-title":"J. Phys.: Condens. Matter"},{"key":"10266_CR19","volume-title":"Analysis of Operators (Methods of Modern Mathematical Physics IV), Acad","author":"M Reed","year":"1978","unstructured":"Reed, M., Simon, B.: Analysis of Operators (Methods of Modern Mathematical Physics IV), Acad. Press, Orlando (1978)"},{"key":"10266_CR20","doi-asserted-by":"crossref","unstructured":"S\u00fcli, E., Mayers, D.F.: An Introduction to Numerical Analysis. Cambridge University Press (2003)","DOI":"10.1017\/CBO9780511801181"},{"issue":"3","key":"10266_CR21","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1137\/130932132","volume":"56","author":"LN Trefethen","year":"2014","unstructured":"Trefethen, L.N., Weideman, J.A.C.: The exponentially convergent trapezoidal rule. SIAM Rev. 56(3), 385\u2013458 (2014)","journal-title":"SIAM Rev."},{"key":"10266_CR22","doi-asserted-by":"crossref","unstructured":"Vanderbilt, D.: Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators. Cambridge University Press (2018)","DOI":"10.1017\/9781316662205"},{"issue":"23","key":"10266_CR23","doi-asserted-by":"publisher","first-page":"2747","DOI":"10.1103\/PhysRevLett.62.2747","volume":"62","author":"J Zak","year":"1989","unstructured":"Zak, J.: Berry\u2019s phase for energy bands in solids. Phys. Rev. Lett. 62(23), 2747 (1989)","journal-title":"Phys. Rev. Lett."},{"key":"10266_CR24","unstructured":"Zhang, H.: Constructing optimal Wannier functions via potential theory: Isolated single band for matrix models. arXiv:2502.08641 (2025)"},{"key":"10266_CR25","doi-asserted-by":"crossref","unstructured":"Zygmund, A.: Trigonometric Series, vol.\u00a01. Cambridge University Press (2002)","DOI":"10.1017\/CBO9781316036587"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-025-10266-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10444-025-10266-4","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-025-10266-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T12:03:38Z","timestamp":1767960218000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10444-025-10266-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,28]]},"references-count":25,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["10266"],"URL":"https:\/\/doi.org\/10.1007\/s10444-025-10266-4","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,28]]},"assertion":[{"value":"20 March 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 October 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 October 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"52"}}