BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar Dualities of spin chains
Dualities of spin chains
Organizers
Lin Zhe Huang , Zheng Wei Liu , Sébastien Palcoux , Yi Long Wang , Jin Song Wu
Speaker
Corey Jones
Time
Wednesday, April 16, 2025 10:30 AM - 12:00 PM
Venue
A3-3-301
Online
Zoom 242 742 6089 (BIMSA)
Abstract
A duality (in the spirit of Kramers-Wannier) is a (locality-preserving) mapping between spin systems that yields a (locality-preserving) isomorphism on a subalgebra of observables containing the terms of the Hamiltonian. The natural subalgebras that arise are called abstract spin chains and are closely connected to the theory of subfactors. A natural question that arises is the problem of classifying dualities up to internal finite-depth circuits. We will explain several invariants arising from subfactor theory and a recent extension result that yields a complete classification in the case where the abstract spin chain is the algebra of symmetric operators under an onsite finite group symmetry. Based on joint work with Kylan Schatz and Dominic Williamson.

Reference:
https://arxiv.org/abs/2410.08884