Quantum phase transitions in one-dimensional nanostructures: a comparison between DFT and DMRG methodologies

Quantum phase transitions in one-dimensional nanostructures: a comparison between DFT and DMRG methodologies | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Quantum phase transitions in one-dimensional nanostructures: a comparison between DFT and DMRG methodologies T. Pauletti, M. Sanino, L. Gimenes, I. M. Carvalho, V. V. França This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3959635/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 16 Jul, 2024 Read the published version in Journal of Molecular Modeling → Version 1 posted 8 You are reading this latest preprint version Abstract Context: In the realm of quantum chemistry, the accurate prediction of electronic structure and properties of nanostructures remains a formidable challenge. Density Functional Theory (DFT) and Density Matrix Renormalization Group (DMRG) have emerged as two powerful computational methods for addressing electronic correlation effects in diverse molecular systems. We compare ground-state energies ( e 0 ), density profiles ( n ) and average entanglement entropies ($\bar S$) in metals, insulators and at the transition from metal to insulator, in homogeneous, superlattices and harmonically confined chains described by the fermionic one-dimensional Hubbard model. While for the homogeneous systems there is a clear hierarchy between the deviations, $D%(\bar S)<D%(e_0)< \bar D%(n)$, and all the deviations decrease with the chain size; for superlattices and harmonical confinement the relation among the deviations is less trivial and strongly dependent on the superlattice structure and the confinement strength considered. For the superlattices, in general increasing the number of impurities in the unit cell represents less precision on the DFT calculations. For the confined chains, DFT performs better for metallic phases, while the highest deviations appear for the Mott and band-insulator phases. This work provides a comprehensive comparative analysis of these methodologies, shedding light on their respective strengths, limitations, and applications. Methods: The DFT calculations were performed using the standard Kohn-Sham scheme within the BALDA approach. It integrated the numerical Bethe-Ansatz (BA) solution of the Hubbard model as the homogeneous density functional within a local-density approximation (LDA) for the exchange-correlation energy. The DMRG algorithms were implemented using the ITensor library, which is based on the Matrix Product States (MPS) ansatz. The calculations were performed until the energy reaches convergence of at least 10 -8 . Density Functional Theory Density Matrix Renormalization Group Hubbard Model Quantum Phase Transitions Entanglement. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 16 Jul, 2024 Read the published version in Journal of Molecular Modeling → Version 1 posted Editorial decision: Revision requested 07 Apr, 2024 Reviews received at journal 11 Mar, 2024 Reviewers agreed at journal 05 Mar, 2024 Reviewers agreed at journal 26 Feb, 2024 Reviewers invited by journal 22 Feb, 2024 Editor assigned by journal 21 Feb, 2024 Submission checks completed at journal 20 Feb, 2024 First submitted to journal 15 Feb, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3959635","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":274131920,"identity":"ae8f6a63-9ba1-4169-aaee-3790577dc583","order_by":0,"name":"T. 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Density Functional Theory (DFT) and Density Matrix Renormalization Group (DMRG) have emerged as two powerful computational methods for addressing electronic correlation effects in diverse molecular systems. We compare ground-state energies (\u003cstrong\u003ee\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/sub\u003e), density profiles (\u003cem\u003e\u003cstrong\u003en\u003c/strong\u003e\u003c/em\u003e) and average entanglement entropies ($\\bar S$) in metals, insulators and at the transition from metal to insulator, in homogeneous, superlattices and harmonically confined chains described by the fermionic one-dimensional Hubbard model. While for the homogeneous systems there is a clear hierarchy between the deviations, $D%(\\bar S)\u0026lt;D%(e_0)\u0026lt; \\bar D%(n)$, and all the deviations decrease with the chain size; for superlattices and harmonical confinement the relation among the deviations is less trivial and strongly dependent on the superlattice structure and the confinement strength considered. For the superlattices, in general increasing the number of impurities in the unit cell represents less precision on the DFT calculations. For the confined chains, DFT performs better for metallic phases, while the highest deviations appear for the Mott and band-insulator phases. 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