Local disorder, topological ground state degeneracy and entanglement entropy, and discrete anyons

Abstract

In this comprehensive study of Kitaev's abelian models defined on a graph embedded on a closed orientable surface, we provide complete proofs of the topological ground state degeneracy, the absence of local order parameters, compute the entanglement entropy exactly and characterise the elementary anyonic excitations. The homology and cohomolgy groups of the cell complex play a central role and allow for a rigorous understanding of the relations between the above characterisations of topological order.

References in corpus (7)

• Criticality, the area law, and the computational power of PEPS
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Ground state entanglement and geometric entropy in the Kitaev's model
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• The complete set of infinite volume ground states for Kitaev's abelian quantum double models
• Kitaev's quantum double model from a local quantum physics point of view
• Jones index, secret sharing and total quantum dimension

Cited by in corpus (7)

• Kitaev's quantum double model as an error correcting code
• The complete set of infinite volume ground states for Kitaev's abelian quantum double models
• Correlation inequalities for classical and quantum XY models
• Properties of 2D anyon gas
• Dynamical abelian anyons with bound states and scattering states
• A 3D lattice defect and efficient computations in topological MBQC
• Topologically ordered states in infinite quantum spin systems