Non-invertible symmetry breaking in a frustration-free spin chain

TL;DR

This paper studies a frustration-free spin-1/2 chain with rank 1 projectors, revealing it is gapped with two ferromagnetic-like ground states that spontaneously break a non-invertible symmetry, using algebraic quantum theory.

Contribution

It demonstrates the existence of a gapped frustration-free spin chain with non-invertible symmetry breaking, a novel example not arising from duality.

Findings

System is gapped with two ground states.

Ground states spontaneously break non-invertible symmetry.

Non-invertible symmetries do not originate from duality.

Abstract

A nearest-neighbor, frustration-free spin $\frac{1}{2}$ chain can be constructed {\it via} projectors of various ranks \'{a} la Bravyi-Gosset. We show that in the rank 1 case this system is gapped and has two ground states resembling ferromagnetic states. These states spontaneously break the non-invertible symmetry connecting them. The latter is proved using the machinery of algebraic quantum theory. The non-invertible symmetries of this system do not come from a duality.