Speaker: Sal Pace (MIT)
Title: Â Lattice T-duality from non-invertible symmetries in quantum spin chains
Abstract: Dualities of quantum field theories are challenging to realize in lattice models of qubits. In this talk, we will explore one of the simplest dualities, T-duality of the compact boson CFT, and its realization in quantum spin chains. In the special case of the XX model, we will discuss an exact lattice T-duality, which is associated with a non-invertible symmetry that exchanges two lattice U(1) symmetries. These U(1) symmetries flow to the momentum and winding symmetries in the CFT. However, their charge operators on the lattice do not commute and instead generate the Onsager algebra. Nevertheless, many features of the anomalies in the CFT are still exactly realized on the lattice, and the lattice U(1) symmetries enforce gaplessness. Indeed, we further explore lattice deformations of the XX model preserving both U(1) symmetries and lattice T-duality and find a rich gapless phase diagram. This talk will be based on arXiv:2409.12220 and arXiv:2412.18606 with Arkya Chatterjee and Shu-Heng Shao.