{"id":396422,"date":"2017-04-11T02:00:00","date_gmt":"2017-04-10T23:00:00","guid":{"rendered":"https:\/\/www.fyysika.ee\/?guid=b22bff29d46a820d52a01d1006d12e8e"},"modified":"2017-04-11T02:00:00","modified_gmt":"2017-04-10T23:00:00","slug":"an-exact-sum-rule-for-the-hubbard-model-an-historicalpedagogical-approach-2","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=396422","title":{"rendered":"An exact sum-rule for the Hubbard model: an historical\/pedagogical approach"},"content":{"rendered":"<p>The aim of the present article is to derive an exact integral equation for the Green function of the<br \/>\nHubbard model through an equation-of-motion procedure, like in the original Hubbard papers. Though<br \/>\nour exact integral equation does not allow to solve the Hubbard model, it represents a strong<br \/>\nconstraint on its approximate solutions. An analogous sum rule has been already obtained in the<br \/>\nliterature, through the use of a spectral moment technique. We think however that our<br \/>\nequation-of-motion procedure can be more easily related to the historical procedure of the original<br \/>\nHubbard papers. We also discuss examples of possible applications of the sum rule and propose and<br \/>\nanalyse a solution, fulfilling it, that can be used for a pedagogical introduction to the<br \/>\nMott\u2013Hubbard metal-insulator transition.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The aim of the present article is to derive an exact integral equation for the Green function of the<br \/>\nHubbard model through an equation-of-motion procedure, like in the original Hubbard papers. Though<br \/>\nour exact integral equation does not allow to solv&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-396422","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/396422","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=396422"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/396422\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=396422"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=396422"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=396422"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}