{"663412":{"#nid":"663412","#data":{"type":"event","title":"PhD Defense by Wangwei Lan","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ESchool of Physics Thesis Dissertation Defense\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EPresenter\u003C\/strong\u003E:\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Wangwei Lan\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ETitle\u003C\/strong\u003E:\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; More efficient contraction algorithms for 2D tensor networks\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EDate\/Time\u003C\/strong\u003E:\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Monday, November 28, 2022 at 1:00 p.m.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ELocation\u003C\/strong\u003E:\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Howey N201\/202\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EVirtual Link\u003C\/strong\u003E:\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; \u003Ca href=\u0022https:\/\/gatech.zoom.us\/j\/2500120410?pwd=RXFXMWFBeGl2RHBqWlRsL25uVitZZz09\u0022\u003Ehttps:\/\/gatech.zoom.us\/j\/2500120410?pwd=RXFXMWFBeGl2RHBqWlRsL25uVitZZz09\u003C\/a\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EMeeting ID: 250 012 0410 \/ Passcode: 765708\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ECommittee\u003C\/strong\u003E:\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Dr. Glen Evenbly, School of Physics, Georgia Institute of Technology (Advisor)\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Zhigang Jiang, School of Physics, Georgia Institute of Technology\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Martin Mourigal, School of Physics, Georgia Institute of Technology\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Dragomir Davidovic, School of Physics, Georgia Institute of Technology\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Spencer Bryngelson, School of Computational Science and Engineering, Georgia Institute of Technology\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EAbstract\u003C\/strong\u003E:\u003C\/p\u003E\r\n\r\n\u003Cp\u003ETensor network algorithms are important numerical tools for studying quantum many-body\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eproblems. However, the high computational costs have prevented its applications in two-\u003C\/p\u003E\r\n\r\n\u003Cp\u003Edimensional (2D) systems. In this thesis, we discussed our work on more efficient con-\u003C\/p\u003E\r\n\r\n\u003Cp\u003Etractions of 2D tensor networks. In particular, for 2D statistical mechanics, we propose\u003C\/p\u003E\r\n\r\n\u003Cp\u003Ea modified form of a tensor renormalization group algorithm for evaluating partition func-\u003C\/p\u003E\r\n\r\n\u003Cp\u003Etions of classical statistical mechanical models on 2D lattices. This algorithm coarse-grains\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eonly the rows and columns of the lattice adjacent to a single core tensor at each step, such\u003C\/p\u003E\r\n\r\n\u003Cp\u003Ethat the lattice size shrinks linearly with the number of coarse-graining steps as opposed\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eto shrinking exponentially as in the usual tensor renormalization group (TRG). However,\u003C\/p\u003E\r\n\r\n\u003Cp\u003Ethe cost of this new approach only scales as O(\u0026chi;4) in terms of the bond dimension \u0026chi;, sig-\u003C\/p\u003E\r\n\r\n\u003Cp\u003Enificantly cheaper than the O(\u0026chi;6) cost scaling of TRG, whereas numerical benchmarking\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eindicates that both approaches have comparable accuracy for the same bond dimension \u0026chi;.\u003C\/p\u003E\r\n\r\n\u003Cp\u003EIn 2D quantum mechanics, we propose a pair of approximations that allows the leading\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eorder computational cost of contracting an infinite projected entangled-pair state (iPEPS)\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eto be reduced from O(\u0026chi;3D6) to O(\u0026chi;3D3) when using a corner-transfer approach. The first\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eapproximation involves (i) reducing the environment needed for truncation of the bound-\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eary tensors (ii) relies on the sequential contraction and truncation of bra and ket indices,\u003C\/p\u003E\r\n\r\n\u003Cp\u003Erather than doing both together as with the established algorithm. Our benchmark results\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eare comparable to the standard iPEPS algorithm. The improvement in computational cost\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eenables us to perform large bond dimension calculations, extending its potential to solve\u003C\/p\u003E\r\n\r\n\u003Cp\u003Echallenging problems.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"More efficient contraction algorithms for 2D tensor networks"}],"uid":"27707","created_gmt":"2022-11-22 18:39:48","changed_gmt":"2022-11-22 18:39:48","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2022-11-28T13:00:00-05:00","event_time_end":"2022-11-28T15:00:00-05:00","event_time_end_last":"2022-11-28T15:00:00-05:00","gmt_time_start":"2022-11-28 18:00:00","gmt_time_end":"2022-11-28 20:00:00","gmt_time_end_last":"2022-11-28 20:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"221981","name":"Graduate Studies"}],"categories":[],"keywords":[{"id":"100811","name":"Phd Defense"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1788","name":"Other\/Miscellaneous"}],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"},{"id":"78771","name":"Public"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}