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 |
Attachments |
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