{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/275725"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/275725","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Application of quantum Monte Carlo methods to homogeneous electron and electron-hole systems","abstract":"The properties of the macroscopic world around us, and of which we are a part, are largely determined by the low energy, collective behaviour of many interacting particles, including the nuclei and, especially, the electrons present. Although the fundamental laws governing the behaviour of these many-body systems are believed to be known in principle, the practical solution of the equations of quantum mechanics remains a challenging area of research. This thesis is concerned with the application of quantum Monte Carlo methods to two model systems: the spin-polarised homogeneous electron gas, and a hole-doped electron gas. Electronic structure theory is briefly reviewed before discussing in more detail the quantum Monte Carlo methods used in this thesis. A study of the three-dimensional spin-polarised homogeneous electron gas (HEG) is then reported, where the relatively new technique of twist averaging is investigated in detail and accurate energies and pair correlation functions are obtained over densities $r_s = 0.5 – 20$ a.u. and the full range of spin-polarisation, allowing comparison with the Perdew-Zunger interpolation scheme used in local spin density approximation exchange-correlation functionals. Following this, an impurity is added to the electron gas in the form of a positively charged hole, and the interaction is studied. Relaxation energies, pair correlation functions and momentum densities are reported. Trion formation is observed over a range of carrier densities and electron-hole mass ratios in agreement with experiment. Isolated trions are also studied, where the diffusion Monte Carlo method is exact. Methodological innovations developed while carrying out this work are discussed, including a variance reduction technique for twist-averaged calculations and a new trial wave function for impurity-in-HEG calculations.","abstract_html":"The properties of the macroscopic world around us, and of which we are a part, are largely determined by the low energy, collective behaviour of many interacting particles, including the nuclei and, especially, the electrons present. Although the fundamental laws governing the behaviour of these many-body systems are believed to be known in principle, the practical solution of the equations of quantum mechanics remains a challenging area of research. This thesis is concerned with the application of quantum Monte Carlo methods to two model systems: the spin-polarised homogeneous electron gas, and a hole-doped electron gas. Electronic structure theory is briefly reviewed before discussing in more detail the quantum Monte Carlo methods used in this thesis. A study of the three-dimensional spin-polarised homogeneous electron gas (HEG) is then reported, where the relatively new technique of twist averaging is investigated in detail and accurate energies and pair correlation functions are obtained over densities <span class=\"etd-inline-math\">r<sub>s</sub> = 0.5 – 20</span> a.u. and the full range of spin-polarisation, allowing comparison with the Perdew-Zunger interpolation scheme used in local spin density approximation exchange-correlation functionals. Following this, an impurity is added to the electron gas in the form of a positively charged hole, and the interaction is studied. Relaxation energies, pair correlation functions and momentum densities are reported. Trion formation is observed over a range of carrier densities and electron-hole mass ratios in agreement with experiment. Isolated trions are also studied, where the diffusion Monte Carlo method is exact. Methodological innovations developed while carrying out this work are discussed, including a variance reduction technique for twist-averaged calculations and a new trial wave function for impurity-in-HEG calculations.","abstract_has_math":true,"creators":["Spink, Graham George"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Needs, Richard"],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-12-22","date_published":"2017-12-22","updated_at":"2026-07-22T22:24:03Z","subjects":["Quantum Monte Carlo","Homoegeneous electron gas","Jellium","Uniform electron gas","Trion","Exciton","Electronic structure","Quantum well"],"languages":["en"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/5f5912e0-b2bb-4031-90c0-eb8bd44d46c4/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.22988","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Needs, Richard"]},{"key":"dc:contributor.sponsor","label":"Sponsor","values":["Financial support provided by the Engineering and Physical Sciences Research Council (EPSRC)"]},{"key":"dc:creator","label":"Author","values":["Spink, Graham George"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2017-12-22"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/275725"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Quantum Monte Carlo","Homoegeneous electron gas","Jellium","Uniform electron gas","Trion","Exciton","Electronic structure","Quantum well"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/5f5912e0-b2bb-4031-90c0-eb8bd44d46c4/download","https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.17863/CAM.22988"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/b90d5707-c924-42d7-b4bc-7ad86dc99794/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The properties of the macroscopic world around us, and of which we are a part, are largely determined by the low energy, collective behaviour of many interacting particles, including the nuclei and, especially, the electrons present. Although the fundamental laws governing the behaviour of these many-body systems are believed to be known in principle, the practical solution of the equations of quantum mechanics remains a challenging area of research. This thesis is concerned with the application of quantum Monte Carlo methods to two model systems: the spin-polarised homogeneous electron gas, and a hole-doped electron gas. Electronic structure theory is briefly reviewed before discussing in more detail the quantum Monte Carlo methods used in this thesis. A study of the three-dimensional spin-polarised homogeneous electron gas (HEG) is then reported, where the relatively new technique of twist averaging is investigated in detail and accurate energies and pair correlation functions are obtained over densities $r_s = 0.5 – 20$ a.u. and the full range of spin-polarisation, allowing comparison with the Perdew-Zunger interpolation scheme used in local spin density approximation exchange-correlation functionals. Following this, an impurity is added to the electron gas in the form of a positively charged hole, and the interaction is studied. Relaxation energies, pair correlation functions and momentum densities are reported. Trion formation is observed over a range of carrier densities and electron-hole mass ratios in agreement with experiment. Isolated trions are also studied, where the diffusion Monte Carlo method is exact. Methodological innovations developed while carrying out this work are discussed, including a variance reduction technique for twist-averaged calculations and a new trial wave function for impurity-in-HEG calculations."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["87eda9de84448d1f82354d60eee3eb5f","07c115680ca8bffdced5487f25c8e7f4"]},{"key":"dc:title","label":"Title","values":["Application of quantum Monte Carlo methods to homogeneous electron and electron-hole systems"]}]}],"canonical_facts":{"dc:contributor.advisor":["Needs, Richard"],"dc:contributor.sponsor":["Financial support provided by the Engineering and Physical Sciences Research Council (EPSRC)"],"dc:creator":["Spink, Graham George"],"dc:date.issued":["2017-12-22"],"dc:description.abstract":["The properties of the macroscopic world around us, and of which we are a part, are largely determined by the low energy, collective behaviour of many interacting particles, including the nuclei and, especially, the electrons present. 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Following this, an impurity is added to the electron gas in the form of a positively charged hole, and the interaction is studied. Relaxation energies, pair correlation functions and momentum densities are reported. Trion formation is observed over a range of carrier densities and electron-hole mass ratios in agreement with experiment. Isolated trions are also studied, where the diffusion Monte Carlo method is exact. Methodological innovations developed while carrying out this work are discussed, including a variance reduction technique for twist-averaged calculations and a new trial wave function for impurity-in-HEG calculations."],"dc:format.checksum.md5":["87eda9de84448d1f82354d60eee3eb5f","07c115680ca8bffdced5487f25c8e7f4"],"dc:identifier.doi":["10.17863/CAM.22988"],"dc:identifier.uri":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/b90d5707-c924-42d7-b4bc-7ad86dc99794/download"],"dc:language":["en"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["https://www.repository.cam.ac.uk/handle/1810/275725"],"dc:rights":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/5f5912e0-b2bb-4031-90c0-eb8bd44d46c4/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"dc:subject":["Quantum Monte Carlo","Homoegeneous electron gas","Jellium","Uniform electron gas","Trion","Exciton","Electronic structure","Quantum well"],"dc:title":["Application of quantum Monte Carlo methods to homogeneous electron and electron-hole systems"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-22T22:24:03Z"}