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DTSTART;TZID=America/New_York:20260127T161500
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SUMMARY:The Quasi-Adiabatic Theorem and All That
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Daniel Spiegel\, Harvard \nTitle: The Quasi-Adiabatic Theorem and All That \nAbstract: Yosuke Kubota has recently made progress on understanding Kitaev’s conjecture by constructing a loop spectrum consisting of spaces of quantum spin systems\, indexed by spatial dimension of the lattice (arXiv: 2503.12618). After a brief reminder on the C*-algebraic formalism of quantum spin systems\, I will discuss Section 2 of this paper\, which covers some of the more analytical tools used to construct the loop spectrum. In particular\, I will focus on the quasi-adiabatic theorem which roughly speaking states that a smooth path of gapped Hamiltonians with unique ground states gives rise to a path of nice automorphisms that map the ground state at time zero to the path of ground states.
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_12726/
LOCATION:Science Center 507\, 1 Oxford Street\, Cambridge\, 02138
CATEGORIES:Geometry and Quantum Theory Seminar
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