Incorporating non-local anyonic statistics into a graph decomposition

2024/01/12 by Matthias Mühlhauser, Mühlhauser, M., V. Kott +3 · 1 citation
Physics and Astronomy · #Advanced Condensed Matter Physics #Atomic and Subatomic Physics Research #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)

paper · pdf · doi:10.48550/arxiv.2401.06507

openalex publication_date 2024/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this work we describe how to systematically implement a full graph decomposition to set up a linked-cluster expansion for the topological phase of Kitaev's toric code in a field. This demands to include the non-local effects mediated by the mutual anyonic statistics of elementary charge and flux excitations. Technically, we describe how to consistently integrate such non-local effects into a hypergraph decomposition for single excitations. The approach is demonstrated for the ground-state energy and the elementary excitation energies of charges and fluxes in the perturbed topological phase.

Cited by

• Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet

Related

• Independent e- and m-anyon confinement in the parallel field toric code on non-square lattices
• Partial Anyon Condensation in the Color Code: A Hamiltonian Approach
• Topology-Aware Exploration of Energy-Based Models Equilibrium: Toric QC-LDPC Codes and Hyperbolic MET QC-LDPC Codes
• Extended string-net models with all anyons at finite temperature
• Anyon Quasilocalization in a Quasicrystalline Toric Code