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Extending the planar theory of anyons to quantum wire networks
by Tomasz Maciazek , Aaron Conlon, Gert Vercleyen, Johannes K. Slingerland
Submission summary
Authors (as registered SciPost users):  Aaron Conlon 
Submission information  

Preprint Link:  scipost_202304_00011v1 (pdf) 
Date submitted:  20230411 18:12 
Submitted by:  Conlon, Aaron 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
The braiding of the worldlines of particles restricted to move on a network (graph) is governed by the graph braid group, which can be strikingly different from the standard braid group known from twodimensional physics. It has been recently shown that imposing the compatibility of graph braiding with anyon fusion for anyons exchanging at a single wire junction leads to new types of anyon models with the braiding exchange operators stemming from solutions of certain generalised hexagon equations. In this work, we establish these graphbraided anyon fusion models for general wire networks. We show that the character of braiding strongly depends on the graphtheoretic connectivity of the given network. In particular, we prove that triconnected networks yield the same braiding exchange operators as the planar anyon models. In contrast, modular biconnected networks support independent braiding exchange operators in different modules. Consequently, such modular networks may lead to more efficient topological quantum computer circuits. Finally, we conjecture that the graphbraided anyon fusion models will possess the (generalised) coherence property where certain polygon equations determine the braiding exchange operators for an arbitrary number of anyons. We also extensively study solutions to these polygon equations for chosen lowrank fusion rings, including the Ising theory, quantum doubles of groups, and TambaraYamagami models. We find numerous solutions that do not appear in the planar theory of anyons.