Majorana Fermions, Exact Mappings between Classical and Topological Orders

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.

5 pages, 4 figures

References in corpus (1)

• Nature of the Quantum Phase Transition in Quantum Compass Model

Cited by in corpus (8)

• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Emergent Fermions and Anyons in the Kitaev Model
• A $\Gamma$-matrix generalization of the Kitaev model
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Reduced fidelity in topological quantum phase transitions