Majorana Fermions, Exact Mappings between Classical and Topological Orders

TL;DR

This paper introduces a novel approach to constructing two-dimensional topological orders from classical symmetry-breaking models, revealing key features like ground state degeneracy and boundary Majorana fermions.

Contribution

It establishes a new method to relate classical orders to topological orders using duality and Majorana fermions, expanding the understanding of topological phases.

Findings

Topological ground state degeneracy depends on topology

Unpaired Majorana fermions appear on boundaries

Two-point correlation functions vanish in the topological phase

Abstract

Motivated by the duality between site-centered spin and bond-centered spin in one-dimensional system, which connects two different constructions of fermions from the same set of Majorana fermions, we show that two-dimensional models with topological orders can be constructed from certain well-known models with classical orders characterized by symmetry-breaking. Topology-dependent ground state degeneracy, vanishing two-point correlation functions, and unpaired Majorana fermions on boundaries emerge naturally from such construction. The approach opens a new way to construct and characterize topological orders.