Qualitative breakdown of the non-crossing approximation for the symmetric one-channel Anderson impurity model at all temperatures

The Anderson impurity model is studied by means of the self-consistent hybridization expansions in its non-crossing (NCA) and one-crossing (OCA) approximations. We have found that for the one-channel spin-\(1/2\) particle-hole symmetric Anderson model, the NCA results are qualitatively wrong for any...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2016-08
Hauptverfasser: Sposetti, C N, Manuel, L O, Roura-Bas, P
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Sposetti, C N
Manuel, L O
Roura-Bas, P
description The Anderson impurity model is studied by means of the self-consistent hybridization expansions in its non-crossing (NCA) and one-crossing (OCA) approximations. We have found that for the one-channel spin-\(1/2\) particle-hole symmetric Anderson model, the NCA results are qualitatively wrong for any temperature, even when the approximation gives the exact threshold exponents of the ionic states. Actually, the NCA solution describes an overscreened Kondo effect, because it is the same as for the two-channel infinite-\(U\) single level Anderson model. We explicitly show that the NCA is unable to distinguish between these two very different physical systems, independently of temperature. Using the impurity entropy as an example, we show that the low temperature values of the NCA entropy for the symmetric case yield the limit \(S_{imp}(T=0)\rightarrow \ln\sqrt{2},\) which corresponds to the zero temperature entropy of the overscreened Kondo model. Similar pathologies are predicted for any other thermodynamic property. On the other hand, we have found that the OCA approach lifts the artificial mapping between the models and restores correct properties of the ground-state, for instance, a vanishing entropy at low enough temperatures \(S_{imp}(T=0)\rightarrow0\). Our results indicate that the very well known NCA should be used with caution close to the symmetric point of the Anderson model.
doi_str_mv 10.48550/arxiv.1608.03018
format Article
fullrecord <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_1608_03018</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2080600085</sourcerecordid><originalsourceid>FETCH-LOGICAL-a525-227b6111f99acaca02bad132719b06d2015dc701931f7dc7b4e22c92975082343</originalsourceid><addsrcrecordid>eNotkE1rwzAMhs1gsNLtB-w0w87pZDnOx7GUfUFhDHoPTuKs7hI7s52uPe6fz2uHDhLiQeh9CLllsEgLIeBBuoPeL1gGxQI4sOKCzJBzlhQp4hW58X4HAJjlKASfkZ_3SfY6yKD3itZOyc_WfhtqOxq2ihprksZZ77X5oHIcnT3oIbLW0M66E-KPw6CC0w21RiXNVhqjero0rXI-YnoYJ6fDkQ62jXsZqOx7GtQwKifD5JS_Jped7L26-e9zsnl63KxekvXb8-tquU6kQJEg5nXGGOvKUjaxAGvZMo45K2vIWgQm2iYHVnLW5XGqU4XYlFjmAgrkKZ-Tu_PZk59qdDGIO1Z_nqqTp0jcn4kY82tSPlQ7OzkTf6oQCsiitkLwX6LEbUU</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2080600085</pqid></control><display><type>article</type><title>Qualitative breakdown of the non-crossing approximation for the symmetric one-channel Anderson impurity model at all temperatures</title><source>arXiv.org</source><source>Freely Accessible Journals at publisher websites</source><creator>Sposetti, C N ; Manuel, L O ; Roura-Bas, P</creator><creatorcontrib>Sposetti, C N ; Manuel, L O ; Roura-Bas, P</creatorcontrib><description>The Anderson impurity model is studied by means of the self-consistent hybridization expansions in its non-crossing (NCA) and one-crossing (OCA) approximations. We have found that for the one-channel spin-\(1/2\) particle-hole symmetric Anderson model, the NCA results are qualitatively wrong for any temperature, even when the approximation gives the exact threshold exponents of the ionic states. Actually, the NCA solution describes an overscreened Kondo effect, because it is the same as for the two-channel infinite-\(U\) single level Anderson model. We explicitly show that the NCA is unable to distinguish between these two very different physical systems, independently of temperature. Using the impurity entropy as an example, we show that the low temperature values of the NCA entropy for the symmetric case yield the limit \(S_{imp}(T=0)\rightarrow \ln\sqrt{2},\) which corresponds to the zero temperature entropy of the overscreened Kondo model. Similar pathologies are predicted for any other thermodynamic property. On the other hand, we have found that the OCA approach lifts the artificial mapping between the models and restores correct properties of the ground-state, for instance, a vanishing entropy at low enough temperatures \(S_{imp}(T=0)\rightarrow0\). Our results indicate that the very well known NCA should be used with caution close to the symmetric point of the Anderson model.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1608.03018</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Approximation ; Entropy ; Impurities ; Kondo effect ; Mapping ; Mathematical analysis ; Particle spin ; Physics - Strongly Correlated Electrons ; Temperature</subject><ispartof>arXiv.org, 2016-08</ispartof><rights>2016. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,784,885,27925</link.rule.ids><backlink>$$Uhttps://doi.org/10.1103/PhysRevB.94.085139$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.48550/arXiv.1608.03018$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Sposetti, C N</creatorcontrib><creatorcontrib>Manuel, L O</creatorcontrib><creatorcontrib>Roura-Bas, P</creatorcontrib><title>Qualitative breakdown of the non-crossing approximation for the symmetric one-channel Anderson impurity model at all temperatures</title><title>arXiv.org</title><description>The Anderson impurity model is studied by means of the self-consistent hybridization expansions in its non-crossing (NCA) and one-crossing (OCA) approximations. We have found that for the one-channel spin-\(1/2\) particle-hole symmetric Anderson model, the NCA results are qualitatively wrong for any temperature, even when the approximation gives the exact threshold exponents of the ionic states. Actually, the NCA solution describes an overscreened Kondo effect, because it is the same as for the two-channel infinite-\(U\) single level Anderson model. We explicitly show that the NCA is unable to distinguish between these two very different physical systems, independently of temperature. Using the impurity entropy as an example, we show that the low temperature values of the NCA entropy for the symmetric case yield the limit \(S_{imp}(T=0)\rightarrow \ln\sqrt{2},\) which corresponds to the zero temperature entropy of the overscreened Kondo model. Similar pathologies are predicted for any other thermodynamic property. On the other hand, we have found that the OCA approach lifts the artificial mapping between the models and restores correct properties of the ground-state, for instance, a vanishing entropy at low enough temperatures \(S_{imp}(T=0)\rightarrow0\). Our results indicate that the very well known NCA should be used with caution close to the symmetric point of the Anderson model.</description><subject>Approximation</subject><subject>Entropy</subject><subject>Impurities</subject><subject>Kondo effect</subject><subject>Mapping</subject><subject>Mathematical analysis</subject><subject>Particle spin</subject><subject>Physics - Strongly Correlated Electrons</subject><subject>Temperature</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNotkE1rwzAMhs1gsNLtB-w0w87pZDnOx7GUfUFhDHoPTuKs7hI7s52uPe6fz2uHDhLiQeh9CLllsEgLIeBBuoPeL1gGxQI4sOKCzJBzlhQp4hW58X4HAJjlKASfkZ_3SfY6yKD3itZOyc_WfhtqOxq2ihprksZZ77X5oHIcnT3oIbLW0M66E-KPw6CC0w21RiXNVhqjero0rXI-YnoYJ6fDkQ62jXsZqOx7GtQwKifD5JS_Jped7L26-e9zsnl63KxekvXb8-tquU6kQJEg5nXGGOvKUjaxAGvZMo45K2vIWgQm2iYHVnLW5XGqU4XYlFjmAgrkKZ-Tu_PZk59qdDGIO1Z_nqqTp0jcn4kY82tSPlQ7OzkTf6oQCsiitkLwX6LEbUU</recordid><startdate>20160810</startdate><enddate>20160810</enddate><creator>Sposetti, C N</creator><creator>Manuel, L O</creator><creator>Roura-Bas, P</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>GOX</scope></search><sort><creationdate>20160810</creationdate><title>Qualitative breakdown of the non-crossing approximation for the symmetric one-channel Anderson impurity model at all temperatures</title><author>Sposetti, C N ; Manuel, L O ; Roura-Bas, P</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a525-227b6111f99acaca02bad132719b06d2015dc701931f7dc7b4e22c92975082343</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Approximation</topic><topic>Entropy</topic><topic>Impurities</topic><topic>Kondo effect</topic><topic>Mapping</topic><topic>Mathematical analysis</topic><topic>Particle spin</topic><topic>Physics - Strongly Correlated Electrons</topic><topic>Temperature</topic><toplevel>online_resources</toplevel><creatorcontrib>Sposetti, C N</creatorcontrib><creatorcontrib>Manuel, L O</creatorcontrib><creatorcontrib>Roura-Bas, P</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sposetti, C N</au><au>Manuel, L O</au><au>Roura-Bas, P</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Qualitative breakdown of the non-crossing approximation for the symmetric one-channel Anderson impurity model at all temperatures</atitle><jtitle>arXiv.org</jtitle><date>2016-08-10</date><risdate>2016</risdate><eissn>2331-8422</eissn><abstract>The Anderson impurity model is studied by means of the self-consistent hybridization expansions in its non-crossing (NCA) and one-crossing (OCA) approximations. We have found that for the one-channel spin-\(1/2\) particle-hole symmetric Anderson model, the NCA results are qualitatively wrong for any temperature, even when the approximation gives the exact threshold exponents of the ionic states. Actually, the NCA solution describes an overscreened Kondo effect, because it is the same as for the two-channel infinite-\(U\) single level Anderson model. We explicitly show that the NCA is unable to distinguish between these two very different physical systems, independently of temperature. Using the impurity entropy as an example, we show that the low temperature values of the NCA entropy for the symmetric case yield the limit \(S_{imp}(T=0)\rightarrow \ln\sqrt{2},\) which corresponds to the zero temperature entropy of the overscreened Kondo model. Similar pathologies are predicted for any other thermodynamic property. On the other hand, we have found that the OCA approach lifts the artificial mapping between the models and restores correct properties of the ground-state, for instance, a vanishing entropy at low enough temperatures \(S_{imp}(T=0)\rightarrow0\). Our results indicate that the very well known NCA should be used with caution close to the symmetric point of the Anderson model.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1608.03018</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2016-08
issn 2331-8422
language eng
recordid cdi_arxiv_primary_1608_03018
source arXiv.org; Freely Accessible Journals at publisher websites
subjects Approximation
Entropy
Impurities
Kondo effect
Mapping
Mathematical analysis
Particle spin
Physics - Strongly Correlated Electrons
Temperature
title Qualitative breakdown of the non-crossing approximation for the symmetric one-channel Anderson impurity model at all temperatures
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T07%3A26%3A45IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Qualitative%20breakdown%20of%20the%20non-crossing%20approximation%20for%20the%20symmetric%20one-channel%20Anderson%20impurity%20model%20at%20all%20temperatures&rft.jtitle=arXiv.org&rft.au=Sposetti,%20C%20N&rft.date=2016-08-10&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1608.03018&rft_dat=%3Cproquest_arxiv%3E2080600085%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2080600085&rft_id=info:pmid/&rfr_iscdi=true