Status  Confirmed 
Seminar Series  PTIHES 
Subjects  hepth 
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 categorytheoretic flavour, that leverages wellestablished 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 onedimensional 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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