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DTSTART;TZID=America/New_York:20251007T161500
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SUMMARY:A Classifying Space for Phases of Matrix Product States
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeakers: Daniel Spiegel\, Harvard Math \nTitle: A Classifying Space for Phases of Matrix Product States \nAbstract: Alexei Kitaev has conjectured that there should be a loop spectrum consisting of spaces of gapped invertible quantum spin systems\, indexed by spatial dimension d of the lattice. Motivated by Kitaev’s conjecture\, I will detail a concrete construction of a topological space B consisting of translation invariant injective matrix product states (MPS) of all physical and bond dimensions\, which plays the role Kitaev’s space in dimension d = 1. Having such a space is a useful tool in the discussion of parametrized phases of MPS; in fact it allows us to define a parametrized phase as a homotopy class of maps into B. The space B is constructed as the quotient of a contractible space E of MPS tensors modulo gauge transformations. The projection map from E to B is a quasifibration\, from which we can compute the homotopy groups of the classifying space B by a long exact sequence. In particular\, B has the weak homotopy type K(Z\, 2) x K(Z\, 3)\, shedding light on Kitaev’s conjecture in the context of MPS. \nDaniel Spiegel will speak for 60 minutes. \nSunghyuk Park  (CMSA) will also speak for 15 minutes
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_10725/
LOCATION:Science Center 507\, 1 Oxford Street\, Cambridge\, 02138
CATEGORIES:Geometry and Quantum Theory Seminar
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