Strong zero modes from geometric chirality in quasi-one-dimensional Mott insulators

TL;DR

This paper demonstrates how geometric chirality in three-leg fermionic Mott insulators leads to strong zero modes related to $ ext{Z}_3$ parafermions, with potential implications for quantum information storage.

Contribution

It establishes a connection between chiral Mott insulators and $ ext{Z}_3$ chiral clock models, introducing a lattice model exhibiting strong zero modes at infinite temperature.

Findings

Strong zero modes persist at infinite temperature.

Edge correlators remain stable over exponentially long times.

The lattice model maps to a perturbed $ ext{Z}_3$ chiral clock model.

Abstract

Strong zero modes provide a paradigm for quantum many-body systems to encode local degrees of freedom that remain coherent far from the ground state. Example systems include $\mathbb{Z}_n$ chiral quantum clock models with strong zero modes related to $\mathbb{Z}_n$ parafermions. Here we show how these models and their zero modes arise from geometric chirality in fermionic Mott insulators, focusing on $n=3$ where the Mott insulators are three-leg ladders. We link such ladders to $\mathbb{Z}_3$ chiral clock models by combining bosonization with general symmetry considerations. We also introduce a concrete lattice model which we show to map to the $\mathbb{Z}_3$ chiral clock model, perturbed by the Uimin-Lai-Sutherland Hamiltonian arising via superexchange. We demonstrate the presence of strong zero modes in this perturbed model by showing that correlators of clock operators at the edge remain close to their initial value for times exponentially long in the system size, even at infinite temperature.