{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/31332"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/31332","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Computational Studies of Correlated Electrons in One-Dimension","abstract":"\"We have studied the extended Hubbard and the Peierls-extended Hubbard models in one dimension using primarily computational methods. We discuss the derivation of the models and the computational methods used to study them, focusing primarily on our extensions over existing numerical methods. In particular, we present the construction of \"\"operator-loop\"\" updates for spin-1/2 fermions and the inclusion of electron-phonon interactions in the Stochastic Series Expansion Quantum Monte Carlo method and the use of Quantum Parallel Tempering to improve the quality of the numerical data. For the extended Hubbard model at half-filling, we have confirmed the existence of a recently reported bond-order wave phase for the ground state in a small region of parameter space between the well-known charge- and spin-density wave phases. We have studied in detail the nature of the associated quantum phase transitions between all the phases. Upon doping away from half-filling, the doubly-degenerate, spin and charge gapped long-range-ordered ground states of the model are shown to evolve to a Luther-Emery liquid with no charge gap but a finite spin gap. For the Peierls-extended Hubbard model, which includes both electron-phonon and electron-electron interactions, we have studied the dimerization transition of the half-filled system in the presence of fully quantum mechanical phonons. We show that the transition to a dimerized state occurs only when the electron-phonon coupling exceeds a finite critical value that depends on the bare phonon frequency. This is in contrast to previous studies in similar models with adiabatic phonons that had predicted a dimerized state for arbitrarily small values of the electron-phonon coupling.\"","abstract_html":""We have studied the extended Hubbard and the Peierls-extended Hubbard models in one dimension using primarily computational methods. We discuss the derivation of the models and the computational methods used to study them, focusing primarily on our extensions over existing numerical methods. In particular, we present the construction of ""operator-loop"" updates for spin-1/2 fermions and the inclusion of electron-phonon interactions in the Stochastic Series Expansion Quantum Monte Carlo method and the use of Quantum Parallel Tempering to improve the quality of the numerical data. For the extended Hubbard model at half-filling, we have confirmed the existence of a recently reported bond-order wave phase for the ground state in a small region of parameter space between the well-known charge- and spin-density wave phases. We have studied in detail the nature of the associated quantum phase transitions between all the phases. Upon doping away from half-filling, the doubly-degenerate, spin and charge gapped long-range-ordered ground states of the model are shown to evolve to a Luther-Emery liquid with no charge gap but a finite spin gap. For the Peierls-extended Hubbard model, which includes both electron-phonon and electron-electron interactions, we have studied the dimerization transition of the half-filled system in the presence of fully quantum mechanical phonons. We show that the transition to a dimerized state occurs only when the electron-phonon coupling exceeds a finite critical value that depends on the bare phonon frequency. This is in contrast to previous studies in similar models with adiabatic phonons that had predicted a dimerized state for arbitrarily small values of the electron-phonon coupling."","abstract_has_math":false,"creators":["Sengupta, Pinaki"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Campbell, D.K."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-06-04T18:45:54Z","date_published":"2012-06-04T18:45:54Z","updated_at":"2026-07-22T22:25:30Z","subjects":["extended Hubbard model","Peierls-extended Hubbard model","electron-phonon coupling"],"languages":["en"],"rights":["©2001 Pinaki Sengupta"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["4539097"],"render_values":[{"text":"4539097","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/31332","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Campbell, D.K."]},{"key":"dc:creator","label":"Author","values":["Sengupta, Pinaki"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-06-04T18:45:54Z","10000-01-01","2001"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["extended Hubbard model","Peierls-extended Hubbard model","electron-phonon coupling"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["©2001 Pinaki Sengupta"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["4539097","http://hdl.handle.net/2142/31332"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"We have studied the extended Hubbard and the Peierls-extended Hubbard models in one dimension using primarily computational methods. We discuss the derivation of the models and the computational methods used to study them, focusing primarily on our extensions over existing numerical methods. In particular, we present the construction of \"\"operator-loop\"\" updates for spin-1/2 fermions and the inclusion of electron-phonon interactions in the Stochastic Series Expansion Quantum Monte Carlo method and the use of Quantum Parallel Tempering to improve the quality of the numerical data. For the extended Hubbard model at half-filling, we have confirmed the existence of a recently reported bond-order wave phase for the ground state in a small region of parameter space between the well-known charge- and spin-density wave phases. We have studied in detail the nature of the associated quantum phase transitions between all the phases. Upon doping away from half-filling, the doubly-degenerate, spin and charge gapped long-range-ordered ground states of the model are shown to evolve to a Luther-Emery liquid with no charge gap but a finite spin gap. For the Peierls-extended Hubbard model, which includes both electron-phonon and electron-electron interactions, we have studied the dimerization transition of the half-filled system in the presence of fully quantum mechanical phonons. We show that the transition to a dimerized state occurs only when the electron-phonon coupling exceeds a finite critical value that depends on the bare phonon frequency. This is in contrast to previous studies in similar models with adiabatic phonons that had predicted a dimerized state for arbitrarily small values of the electron-phonon coupling.\"","Submitted by Elizabeth Kent (eckent2@illinois.edu) on 2012-06-04T18:45:54Z No. of bitstreams: 1 2001_sengupta.pdf: 3474727 bytes, checksum: 868cd94bee2d85aaf16ab5da4958d4f2 (MD5)","Made available in DSpace on 2012-06-04T18:45:54Z (GMT). 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We discuss the derivation of the models and the computational methods used to study them, focusing primarily on our extensions over existing numerical methods. In particular, we present the construction of \"\"operator-loop\"\" updates for spin-1/2 fermions and the inclusion of electron-phonon interactions in the Stochastic Series Expansion Quantum Monte Carlo method and the use of Quantum Parallel Tempering to improve the quality of the numerical data. For the extended Hubbard model at half-filling, we have confirmed the existence of a recently reported bond-order wave phase for the ground state in a small region of parameter space between the well-known charge- and spin-density wave phases. We have studied in detail the nature of the associated quantum phase transitions between all the phases. Upon doping away from half-filling, the doubly-degenerate, spin and charge gapped long-range-ordered ground states of the model are shown to evolve to a Luther-Emery liquid with no charge gap but a finite spin gap. For the Peierls-extended Hubbard model, which includes both electron-phonon and electron-electron interactions, we have studied the dimerization transition of the half-filled system in the presence of fully quantum mechanical phonons. We show that the transition to a dimerized state occurs only when the electron-phonon coupling exceeds a finite critical value that depends on the bare phonon frequency. This is in contrast to previous studies in similar models with adiabatic phonons that had predicted a dimerized state for arbitrarily small values of the electron-phonon coupling.\"","Submitted by Elizabeth Kent (eckent2@illinois.edu) on 2012-06-04T18:45:54Z No. of bitstreams: 1 2001_sengupta.pdf: 3474727 bytes, checksum: 868cd94bee2d85aaf16ab5da4958d4f2 (MD5)","Made available in DSpace on 2012-06-04T18:45:54Z (GMT). No. of bitstreams: 1 2001_sengupta.pdf: 3474727 bytes, checksum: 868cd94bee2d85aaf16ab5da4958d4f2 (MD5) Previous issue date: 2001","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Elizabeth Kent (eckent2@illinois.edu) on 2012-06-04T18:45:54Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:34:57-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: thesis","thesis","U of I Only"],"dc:identifier":["4539097","http://hdl.handle.net/2142/31332"],"dc:language":["en"],"dc:rights":["©2001 Pinaki Sengupta"],"dc:subject":["extended Hubbard model","Peierls-extended Hubbard model","electron-phonon coupling"],"dc:title":["Computational Studies of Correlated Electrons in One-Dimension"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:30Z"}