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SUMMARY:Topological Symmetry and Duality in Quantum Lattice Models
DTSTART:20240423T120000Z
DTEND:20240423T140000Z
DTSTAMP:20241004T025300Z
UID:indico-event-11677@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Clément Delcamp (IHES)\n\nA modern perspective on s
ymmetry in quantum theories identifies the topological invariance of a sym
metry operator within correlation functions as its defining property. In a
ddition to suggesting generalised notions of symmetry\, this viewpoint ena
bles a calculus of topological defects\, which has a strong category-theor
etic flavour\, that leverages well-established methods from topological qu
antum field theory. Focusing on finite symmetries\, I will delve during th
ese lectures into a realisation of this program in the context of one-dime
nsional quantum lattice models. Concretely\, I will present a framework fo
r systematically investigating lattice Hamiltonians\, elucidating their sy
mmetry operators\, defining duality/gauging transformations and computing
the mapping of topological sectors through such transformations. Moreover\
, I will comment on the classification of gapped symmetric phases for gene
ralised symmetry and the construction of the corresponding order/disorder
parameters. I will provide explicit treatments of familiar physical system
s from condensed matter theory\, shedding light on celebrated results and
offering resolutions to certain open problems. Time permitting\, I will br
iefly touch upon generalisations to higher dimensions and implications to
numerical simulations. \n\nhttps://indico.math.cnrs.fr/event/11677/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/11677/
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