One dimensional Staggered Bosons, Clock models and their non-invertible symmetries

TL;DR

This paper explores one-dimensional staggered boson and clock models, revealing their non-invertible symmetries related to T-duality, and predicts critical behavior with specific conformal field theories.

Contribution

It uncovers the non-invertible symmetries in staggered boson and clock models and links them to critical points characterized by a $U(1)$ current algebra.

Findings

Non-invertible symmetries are related to T-duality.

Models exhibit criticality with $c=1$ conformal field theory.

Critical points occur at specific radii for $N>4$.

Abstract

We study systems of staggered boson Hamiltonians in a one dimensional lattice and in particular how the translation symmetry by one unit in these systems is in reality a non-invertible symmetry closely related to T-duality. We also study the simplest systems of clock models derived from these staggered boson Hamiltonians. We show that the non-invertible symmetries of these lattice models together with the discrete ${\mathbb Z}_N$ symmetry predict that these are critical points with a $U(1)$ current algebra at $c=1$ and radius $\sqrt{2N}$ whenever $N>4$.