Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Status Confirmed
Seminar Series PT-IHES
Subjects hep-th
Date Friday 3 May 2024
Time 14:00
Institute IHES
Seminar Room Amphithéâtre Léon Motchane
Speaker's Last Name Delcamp
Speaker's First Name Clement
Speaker's Email Address
Speaker's Institution IHES
Title Topological Symmetry and Duality in Quantum Lattice Models (4/4)
Abstract A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. In addition to suggesting generalised notions of symmetry, this viewpoint enables a calculus of topological defects, which has a strong category-theoretic flavour, that leverages well-established methods from topological quantum field theory. Focusing on finite symmetries, I will delve during these lectures into a realisation of this program in the context of one-dimensional quantum lattice models. Concretely, I will present a framework for systematically investigating lattice Hamiltonians, elucidating their symmetry 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 generalised symmetry and the construction of the corresponding order/disorder parameters. I will provide explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Time permitting, I will briefly touch upon generalisations to higher dimensions and implications to numerical simulations.
arXiv Preprint Number
Comments Cours de l'IHES

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