{"id":365118,"date":"2017-02-16T03:00:00","date_gmt":"2017-02-16T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=b16c2903f886cc86b827c4251cdba4f5"},"modified":"2017-02-16T03:00:00","modified_gmt":"2017-02-16T00:00:00","slug":"quantum-phase-transitions-a-variational-mean-field-perspective","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=365118","title":{"rendered":"Quantum phase transitions: a variational mean-field perspective"},"content":{"rendered":"<p>To illustrate a simple mean-field-like approach for examining quantum phase transitions we consider<br \/>\nthe ##IMG## [http:\/\/ej.iop.org\/images\/0143-0807\/38\/3\/033002\/ejpaa5c71ieqn1.gif]<br \/>\n{$J\\mbox{&#8211;}{J}^{\\prime }$} quantum Heisenberg antiferromagnet on a square lattice. The exchange<br \/>\ncouplings J and ##IMG## [http:\/\/ej.iop.org\/images\/0143-0807\/38\/3\/033002\/ejpaa5c71ieqn2.gif]<br \/>\n{${J}^{\\prime }$} are competing with each other. The ratio ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/38\/3\/033002\/ejpaa5c71ieqn3.gif] {${J}^{\\prime }\/J$} is the<br \/>\ncontrol parameter and its change drives the transition. We adopt a variational ansatz, calculate the<br \/>\nground-state energy as well as the order parameter and describe the quantum phase transition<br \/>\ninherent in the model. This description corresponds completely to the standard Landau theory of<br \/>\nphase transitions. We also discuss how to generalize such an approach for more complicated quantum<br \/>\n&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>To illustrate a simple mean-field-like approach for examining quantum phase transitions we consider<br \/>\nthe ##IMG## [http:\/\/ej.iop.org\/images\/0143-0807\/38\/3\/033002\/ejpaa5c71ieqn1.gif]<br \/>\n{$J\\mbox{&#8211;}{J}^{\\prime }$} quantum Heisenberg antiferromagnet on a sq&#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-365118","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\/365118","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=365118"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/365118\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=365118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=365118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=365118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}