MS Seminar (Mathematics - String Theory)

Speaker: Paul Fendley (University of Oxford)
Title: From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible defects
Date (JST): Tue, Jul 04, 2023, 17:00 - 18:00
Place: Zoom
Abstract: Recent work has revealed a host of “dualities” between strongly interacting models. As apparent from the canonical example of Kramers and Wannier, such dualities are much subtler than a one-to-one mapping of energy levels, but rather are non-invertible. I describe an algebraic structure in the XXZ spin chain and three other Hamiltonian that yields non-invertible maps between them and also guarantees all are integrable. The models describe Rydberg-blockade bosons on the ladder constrained to at most one particle per square, a three-state antiferromagnet, and two Ising chains coupled in a zig-zag fashion. The Rydberg and Ising ladders also possess useful non-invertible symmetries, with the spontaneous breaking of one in the former resulting in an unusual ground-state degeneracy. The maps are developed using topological defects coming from fusion categories and the lattice analog of the orbifold construction.
Remarks: Zoom seminar