{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23725"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23725","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A quantum Monte Carlo study of the two-dimensional electron gas","abstract":"Quantum Monte Carlo has recently made great progress as a computational tool for quantum many-body systems. We have extended previous Monte Carlo methods to study both ground state and excited states of the two-dimensional electron gas. For ground state properties we have used variational and fixed-node diffusion Monte Carlo methods, the latter of which is a nearly exact method for a system of many fermions. With introduction of backflow and three-body correlations, we find significant improvements in both variational and fixed-node energies over the Slater-Jastrow results which consider only two-body correlations. It is found that the backflow effect is dominant over the three-body effect at high density ($r\\sb{s} \\sim 1)$ while they are of equal importance at the lowest density considered $(r\\sb{s} \\sim 20)$. The effects are comparable to those in bulk $\\sp3$He. The numerical results are used to provide an analytic expression for the correlation energy of the two-dimensional electron gas as a function of the density. For particle-hole excitations of the system, variational Monte Carlo is employed. Correlated sampling is introduced to calculate small energy differences between different excitations. The usual pair-product (Slater-Jastrow) trial wave function is found to lack certain correlations entirely so that backflow correlation is crucial. From the excitation energies calculated here, we determine Fermi liquid parameters and related physical quantities such as the effective mass and Lande g factor of the two-dimensional electron gas, which are compared with previous analytic calculations. Finally, the validity of our fixed-node calculations for the ground state and variational ones for the excitations is tested by transient-estimate calculations, which allow for relaxation of the fixed-node conditions.","abstract_html":"Quantum Monte Carlo has recently made great progress as a computational tool for quantum many-body systems. We have extended previous Monte Carlo methods to study both ground state and excited states of the two-dimensional electron gas. For ground state properties we have used variational and fixed-node diffusion Monte Carlo methods, the latter of which is a nearly exact method for a system of many fermions. With introduction of backflow and three-body correlations, we find significant improvements in both variational and fixed-node energies over the Slater-Jastrow results which consider only two-body correlations. It is found that the backflow effect is dominant over the three-body effect at high density ($r\\sb{s} \\sim 1)$ while they are of equal importance at the lowest density considered $(r\\sb{s} \\sim 20)$. The effects are comparable to those in bulk $\\sp3$He. The numerical results are used to provide an analytic expression for the correlation energy of the two-dimensional electron gas as a function of the density. For particle-hole excitations of the system, variational Monte Carlo is employed. Correlated sampling is introduced to calculate small energy differences between different excitations. The usual pair-product (Slater-Jastrow) trial wave function is found to lack certain correlations entirely so that backflow correlation is crucial. From the excitation energies calculated here, we determine Fermi liquid parameters and related physical quantities such as the effective mass and Lande g factor of the two-dimensional electron gas, which are compared with previous analytic calculations. Finally, the validity of our fixed-node calculations for the ground state and variational ones for the excitations is tested by transient-estimate calculations, which allow for relaxation of the fixed-node conditions.","abstract_has_math":true,"creators":["Kwon, Yongkyung"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics, Condensed Matter","degree_department":null,"school":null,"contributors":["Martin, Richard M."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T14:24:46Z","date_published":"2011-05-07T14:24:46Z","updated_at":"2026-07-22T22:25:22Z","subjects":["Physics, Condensed Matter"],"languages":["eng"],"rights":["Copyright 1994 Kwon, Yongkyung"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9512442","(UMI)AAI9512442"],"render_values":[{"text":"AAI9512442","href":null,"code":true},{"text":"(UMI)AAI9512442","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23725","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Martin, Richard M."]},{"key":"dc:creator","label":"Author","values":["Kwon, Yongkyung"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T14:24:46Z","10000-01-01","1994"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics, Condensed Matter"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Physics, Condensed Matter"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1994 Kwon, Yongkyung"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9512442","(UMI)AAI9512442","http://hdl.handle.net/2142/23725"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Quantum Monte Carlo has recently made great progress as a computational tool for quantum many-body systems. We have extended previous Monte Carlo methods to study both ground state and excited states of the two-dimensional electron gas. For ground state properties we have used variational and fixed-node diffusion Monte Carlo methods, the latter of which is a nearly exact method for a system of many fermions. With introduction of backflow and three-body correlations, we find significant improvements in both variational and fixed-node energies over the Slater-Jastrow results which consider only two-body correlations. It is found that the backflow effect is dominant over the three-body effect at high density ($r\\sb{s} \\sim 1)$ while they are of equal importance at the lowest density considered $(r\\sb{s} \\sim 20)$. The effects are comparable to those in bulk $\\sp3$He. The numerical results are used to provide an analytic expression for the correlation energy of the two-dimensional electron gas as a function of the density. For particle-hole excitations of the system, variational Monte Carlo is employed. Correlated sampling is introduced to calculate small energy differences between different excitations. The usual pair-product (Slater-Jastrow) trial wave function is found to lack certain correlations entirely so that backflow correlation is crucial. From the excitation energies calculated here, we determine Fermi liquid parameters and related physical quantities such as the effective mass and Lande g factor of the two-dimensional electron gas, which are compared with previous analytic calculations. Finally, the validity of our fixed-node calculations for the ground state and variational ones for the excitations is tested by transient-estimate calculations, which allow for relaxation of the fixed-node conditions.","Made available in DSpace on 2011-05-07T14:24:46Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9512442.pdf: 5790179 bytes, checksum: 21f77ab8610eef3019959271d3cd189b (MD5) Previous issue date: 1994","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:06:25Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:31:53-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["A quantum Monte Carlo study of the two-dimensional electron gas"]}]}],"canonical_facts":{"dc:contributor":["Martin, Richard M."],"dc:creator":["Kwon, Yongkyung"],"dc:date":["2011-05-07T14:24:46Z","10000-01-01","1994"],"dc:description":["Quantum Monte Carlo has recently made great progress as a computational tool for quantum many-body systems. We have extended previous Monte Carlo methods to study both ground state and excited states of the two-dimensional electron gas. For ground state properties we have used variational and fixed-node diffusion Monte Carlo methods, the latter of which is a nearly exact method for a system of many fermions. With introduction of backflow and three-body correlations, we find significant improvements in both variational and fixed-node energies over the Slater-Jastrow results which consider only two-body correlations. It is found that the backflow effect is dominant over the three-body effect at high density ($r\\sb{s} \\sim 1)$ while they are of equal importance at the lowest density considered $(r\\sb{s} \\sim 20)$. The effects are comparable to those in bulk $\\sp3$He. The numerical results are used to provide an analytic expression for the correlation energy of the two-dimensional electron gas as a function of the density. For particle-hole excitations of the system, variational Monte Carlo is employed. Correlated sampling is introduced to calculate small energy differences between different excitations. The usual pair-product (Slater-Jastrow) trial wave function is found to lack certain correlations entirely so that backflow correlation is crucial. From the excitation energies calculated here, we determine Fermi liquid parameters and related physical quantities such as the effective mass and Lande g factor of the two-dimensional electron gas, which are compared with previous analytic calculations. Finally, the validity of our fixed-node calculations for the ground state and variational ones for the excitations is tested by transient-estimate calculations, which allow for relaxation of the fixed-node conditions.","Made available in DSpace on 2011-05-07T14:24:46Z (GMT). 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