{"390901":{"#nid":"390901","#data":{"type":"event","title":"Correlation Diagrams: An Intuitive Approach to Correlations in Quantum Hall Systems","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ESchool of Physics Hard Condensed Matter \u0026amp; AMO Seminar: Prof. John Quinn, University of Tennessee, Knoxville \u003Cbr \/\u003E\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003EA trial wave function \\f (1,2,...,N) of an N electron system can always be written as the product of an antisymmetric Fermion factor F {Zij }= Tii\u0026lt;jZij , and a symmetric correlation factor G {Zij }. F results from Pauli principle, and G is caused by Coulomb interactions. One can represent G diagrammatically ( I J by distributing N points on the circumference of a circle, and drawing appropriate lines representing correlation factors (cfs) Zij between pairs. Here, of course, Zij = Zi\u0026shy;\u0026nbsp;Zj, and Zi is the complex coordinate of the i111 electron. Laughlin correlation for the v=l\/3 filled\u0026nbsp;incompressible quantum liquid (IQL) state contain two cfs\u0026nbsp; connecting each pair i,j. For the Moore-Read state of the half-filled excited Landau level (LL), with v=2 + 1\/ 2, the even value of N for the half-filled LL is partitioned into two subsets A and B, each containing N\/2 electrons[21. font-family:\u0022Arial\u0022,sans-serif\u0022\u0026gt;\u003C\/p\u003E\u003Cp\u003EFor any one partition(A,B)the contribution to G is given by GAB = Tii\u0026lt;ji;Az\\Tik\u0026lt;Ii;sZ2kt \u00b7 The full G is equal to the symmetric sum of contributions GAB over all possible partitions of N into two equal subsets. For Jain states at filling factor v=p\/ \u003Cem\u003Eq \u003C\/em\u003E\u0026lt; 1\/ 2 , the \u0026nbsp;value \u0026nbsp;of \u0026nbsp;the \u0026nbsp;single \u0026nbsp;particle angular momentum \u003Cem\u003Ee \u003C\/em\u003Esatisfies the equation \u0026nbsp;20=v- 1N-Cv, with Cv = q + 1 - p. The values of (2 N)\u0026nbsp;define the function space of G {Zij}, which must satisfy a number of conditions.\u003C\/p\u003E\u003Cp\u003EFor example, the highest power of any Zi cannot exceed 2e+ 1-N. In addition, the value of the total angular momentum L of the lowest correlated state must satisfy the equation L=(N \/ 2) (2e+ 1-N)-Ka, where Ka is the degree of the homogeneous polynomial generated by G. Knowing the values of L for IQL states (and for states containing a few quasielectrons or a few quasiholes) from Jain\u0027s mean field CF picture allows one to determine Ka. The dependence of the pair pseudopotential V(L2) on pair angular momentum L2 , suggests a small number of correlation diagrams \u0026nbsp;for a given value of the total angular momentum L. Correlation diagrams and correlation functions for\u0026nbsp;the Jain state at v=2 \/S and for the Moore-Read stated will be presented as example. 12.0pt;font-family:\u0022Arial\u0022,sans-serif\u0022\u0026gt;\u003C\/p\u003E\u003Cp\u003E[1] J.J. Quinn, Waves in random and complex media (2014) 898867\u003C\/p\u003E\u003Cp\u003E[2] S.B. Mulay, J.J . Quinn, and M.A. Shattuck, submitted to J. Math. Phys. (2014)\u003Cstrong\u003E \u003Cbr \/\u003E\u003C\/strong\u003E\u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Correlation Diagrams: An Intuitive Approach to Correlations in Quantum Hall Systems"}],"uid":"27664","created_gmt":"2015-03-26 11:36:04","changed_gmt":"2016-10-08 01:49:04","author":"Alison Morain","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2015-04-09T15:00:00-04:00","event_time_end":"2015-04-09T16:00:00-04:00","event_time_end_last":"2015-04-09T16:00:00-04:00","gmt_time_start":"2015-04-09 19:00:00","gmt_time_end":"2015-04-09 20:00:00","gmt_time_end_last":"2015-04-09 20:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"126011","name":"School of Physics"}],"categories":[],"keywords":[{"id":"122591","name":"Correlation Diagrams"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1795","name":"Seminar\/Lecture\/Colloquium"}],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[{"value":"\u003Cp\u003E\u003Ca href=\u0022mailto:alison.morain@physics.gatech.edu\u0022\u003Ealison.morain@physics.gatech.edu\u003C\/a\u003E\u003C\/p\u003E","format":"limited_html"}],"email":[],"slides":[],"orientation":[],"userdata":""}}}