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DTSTART;TZID=America/New_York:20220921T090000
DTEND;TZID=America/New_York:20220921T100000
DTSTAMP:20240229T110819Z
CREATED:20230705T064901Z
LAST-MODIFIED:20240229T110819Z
UID:10001142-1663750800-1663754400@cmsa.fas.harvard.edu
SUMMARY:Geometric test for topological states of matter
DESCRIPTION:Topological Quantum Matter Seminar\nSpeaker: Semyon Klevtsov\, University of Strasbourg \nTitle: Geometric test for topological states of matter \nAbstract: We generalize the flux insertion argument due to Laughlin\, Niu-Thouless-Tao-Wu\, and Avron-Seiler-Zograf to the case of fractional quantum Hall states on a higher-genus surface. We propose this setting as a test to characterise the robustness\, or topologicity\, of the quantum state of matter and apply our test to the Laughlin states. Laughlin states form a vector bundle\, the Laughlin bundle\, over the Jacobian – the space of Aharonov-Bohm fluxes through the holes of the surface. The rank of the Laughlin bundle is the \ndegeneracy of Laughlin states or\, in presence of quasiholes\, the dimension of the corresponding full many-body Hilbert space; its slope\, which is the first Chern class divided by the rank\, is the Hall conductance. We compute the rank and all the Chern classes of Laughlin bundles for any genus and any number of quasiholes\, settling\, in particular\, the Wen-Niu conjecture. Then we show that Laughlin bundles with non-localized quasiholes are not projectively flat and that the Hall current is precisely quantized only for the states with localized quasiholes. Hence our test distinguishes these states from the full many-body Hilbert space. Based on joint work with Dimitri Zvonkine (CNRS\, University of Paris-Versaille). \n 
URL:https://cmsa.fas.harvard.edu/event/geometric-test-for-topological-states-of-matter/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topological Quantum Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Topological-Seminar-09.21.22.png
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