Persisting topological order via geometric frustration

TL;DR

This paper introduces a new exactly solvable topological quantum model on the dice lattice, revealing that geometric frustration can robustly preserve topological order even under magnetic perturbations.

Contribution

It establishes a novel connection between topological order and geometric frustration through a solvable lattice model and its mapping to a frustrated Ising model.

Findings

Topological order remains robust under magnetic field due to geometric frustration.

A new exactly solvable model on the dice lattice exhibiting topological order.

Link between frustrated Ising models and topologically ordered systems.

Abstract

We introduce a toric code model on the dice lattice which is exactly solvable and displays topological order at zero temperature. In the presence of a magnetic field, the flux dynamics is mapped to the highly frustrated transverse field Ising model on the kagome lattice. This correspondence suggests an intriguing disorder by disorder phenomenon in a topologically ordered system implying that the topological order is extremely robust due to the geometric frustration. Furthermore, a connection between fully frustrated transverse field Ising models and topologically ordered systems is demonstrated which opens an exciting physical playground due to the interplay of topological quantum order and geometric frustration.