{"id":"https://openalex.org/W2944523898","doi":null,"title":"Exact solution of a time-reversal-invariant topological superconducting wire","display_name":"Exact solution of a time-reversal-invariant topological superconducting wire","publication_year":2019,"publication_date":"2019-05-10","ids":{"openalex":"https://openalex.org/W2944523898","mag":"2944523898"},"language":"en","primary_location":{"id":"mag:2944523898","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1905.04255","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1905.04255","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065468978","display_name":"Armando A. Aligia","orcid":"https://orcid.org/0000-0001-9647-3926","observed_orcids":["https://orcid.org/0000-0001-9647-3926"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. A. Aligia","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-9647-3926","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5024913093","display_name":"Alberto Camjayi","orcid":"https://orcid.org/0009-0001-6078-4535","observed_orcids":["https://orcid.org/0009-0001-6078-4535"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alberto Camjayi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10657","display_name":"Topological Materials and Phenomena","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10657","display_name":"Topological Materials and Phenomena","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.0017999999690800905,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11682","display_name":"Advanced Condensed Matter Physics","score":0.000699999975040555,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/topological-superconductivity","display_name":"topological superconductivity","score":0.8339999914169312},{"id":"https://openalex.org/keywords/time-reversal-invariant-topological-superconductors","display_name":"time-reversal invariant topological superconductors","score":0.953000009059906},{"id":"https://openalex.org/keywords/exact-solutions","display_name":"exact solutions","score":0.6269999742507935},{"id":"https://openalex.org/keywords/zero-modes","display_name":"zero modes","score":0.7400000095367432},{"id":"https://openalex.org/keywords/ground-state-degeneracy","display_name":"ground state degeneracy","score":0.765999972820282},{"id":"https://openalex.org/keywords/entanglement","display_name":"entanglement","score":0.8199999928474426},{"id":"https://openalex.org/keywords/extended-s-wave-pairing","display_name":"extended s-wave pairing","score":0.8679999709129333},{"id":"https://openalex.org/keywords/spin-orbit-coupling","display_name":"spin-orbit coupling","score":0.9980000257492065},{"id":"https://openalex.org/keywords/magnetic-field-effects","display_name":"magnetic field effects","score":0.6290000081062317}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7488828301429749},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.5954273343086243},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.556334376335144},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.49933910369873047},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4844255745410919},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.48341119289398193},{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.4650574326515198},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.44320619106292725},{"id":"https://openalex.org/C54101563","wikidata":"https://www.wikidata.org/wiki/Q124131","display_name":"Superconductivity","level":2,"score":0.44068974256515503},{"id":"https://openalex.org/C125020911","wikidata":"https://www.wikidata.org/wiki/Q1570979","display_name":"Spin\u2013orbit interaction","level":2,"score":0.43043699860572815},{"id":"https://openalex.org/C2780658932","wikidata":"https://www.wikidata.org/wiki/Q8069598","display_name":"Zero mode","level":2,"score":0.4166647791862488},{"id":"https://openalex.org/C137618395","wikidata":"https://www.wikidata.org/wiki/Q576728","display_name":"Winding number","level":2,"score":0.41380006074905396},{"id":"https://openalex.org/C52233224","wikidata":"https://www.wikidata.org/wiki/Q44363","display_name":"Fermion","level":2,"score":0.41149580478668213},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16601985692977905},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15082785487174988},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1319386065006256},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2944523898","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1905.04255","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2944523898","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1905.04255","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2972959835","https://openalex.org/W4391644201","https://openalex.org/W2808095210","https://openalex.org/W2890304931","https://openalex.org/W2742895187","https://openalex.org/W2022476153","https://openalex.org/W3082346470","https://openalex.org/W2593142381","https://openalex.org/W2967076524","https://openalex.org/W1561658376"],"abstract_inverted_index":{"We":[0,31,159,173],"consider":[1,161],"a":[2,7,14,18,89,99,131,136,162,196],"model":[3,38],"proposed":[4],"before":[5],"for":[6,34,112,135,186],"time-reversal-invariant":[8],"topological":[9],"superconductor":[10],"(TRITOPS)":[11],"which":[12],"contains":[13],"hopping":[15,133],"term":[16,134],"$t$,":[17],"chemical":[19],"potential":[20],"$\\mu$,":[21],"an":[22,139,154],"extended":[23],"$s$-wave":[24],"pairing":[25],"$\\Delta$":[26],"and":[27,70,147,179],"spin-orbit":[28,184],"coupling":[29],"$\\lambda$.":[30],"show":[32,80],"that":[33,85],"$|\\Delta|=|\\lambda|$,":[35],"$\\mu=t=0$,":[36],"the":[37,59,68,71,75,83,93,103,124,145,148,171,175,183,190],"can":[39],"be":[40],"solved":[41],"exactly":[42,66],"defining":[43],"new":[44],"fermion":[45],"operators":[46],"involving":[47],"nearest-neighbor":[48],"sites.":[49],"The":[50],"many-body":[51,176],"ground":[52,149],"state":[53,150],"is":[54,96],"four-fold":[55],"degenerate":[56],"due":[57],"to":[58,98,167],"existence":[60],"of":[61,74,130,142,157,170,189],"two":[62],"zero-energy":[63,90],"modes":[64],"localized":[65],"at":[67,92,102],"first":[69,94],"last":[72,104],"site":[73,95],"chain.":[76,172],"These":[77],"four":[78],"states":[79],"entanglement":[81],"in":[82],"sense":[84],"creating":[86],"or":[87],"annihilating":[88],"mode":[91],"proportional":[97],"similar":[100],"operation":[101],"site.":[105],"By":[106],"continuity,":[107],"this":[108],"property":[109],"should":[110],"persist":[111],"general":[113],"parameters.":[114],"Using":[115],"these":[116],"results":[117,194],"we":[118],"correct":[119],"some":[120],"statements":[121],"related":[122],"with":[123,138,153,192],"so":[125],"called":[126],"time-reversal":[127],"anomaly.":[128],"Addition":[129],"small":[132,163,197],"chain":[137,198],"even":[140,155],"number":[141,156],"sites":[143],"breaks":[144],"degeneracy":[146],"becomes":[151],"unique":[152],"particles.":[158],"also":[160],"magnetic":[164],"field":[165],"applied":[166],"one":[168],"end":[169],"compare":[174],"excitation":[177],"energies":[178],"spin":[180],"projection":[181],"along":[182],"direction":[185],"both":[187],"ends":[188],"chains":[191],"numerical":[193],"%for":[195],"obtaining":[199],"good":[200],"agreement.":[201]},"counts_by_year":[],"updated_date":"2026-09-22T06:50:58.402377","created_date":"2019-05-16T00:00:00"}