Scientific Calendar Event



Starts 24 Jan 2023 11:00
Ends 24 Jan 2023 12:00
Central European Time
Hybrid seminar
room 128 (SISSA, via Bonomea) + Zoom

Paul Fendley
(Oxford)


 

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 explain such dualities between four distinct 1d quantum Hamiltonians, including the XXZ chain. I describe a new algebraic structure, and exploit it to find and derive non-invertible maps to three other “dual” integrable Hamiltonians. The new 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 maps are developed using topological defects coming from fusion categories and the lattice analog of the orbifold construction.