Dyonic Sectors and Intertwiner Connections in 2+1-dimensional Lattice Z_N-Higgs Models

TL;DR

This paper constructs dyonic states in 2+1D lattice Z_N-Higgs models, revealing their charge representations, equivalences, and a local intertwiner connection with Z_N phases, laying groundwork for anyon scattering states.

Contribution

It introduces a novel construction of dyonic states with both electric and magnetic charges and develops a local intertwiner connection with Z_N phases in lattice models.

Findings

Charged representations of the observable algebra are constructed.

Representations with coinciding total charges are shown to be equivalent.

A local intertwiner connection with Z_N-valued holonomy is established.

Abstract

We construct dyonic states in 2+1-dimensional lattice Z_N-Higgs models, i.e., states which are both, electrically and magnetically charged. The associated Hilbert spaces carry charged representations of the observable algebra, the global transfer matrix and a unitary implementation of the group of spatial lattice translations. We prove that for coinciding total charges these representations are dynamically equivalent and we construct a local intertwiner connection depending on a path in the space of charge distributions. The holonomy of this connection is given by Z_N-valued phases. This will be the starting point for a construction of scattering states with anyon statistics in a subsequent paper.