A chain of strongly correlated SU(2)_4 anyons: Hamiltonian and Hilbert space of states

TL;DR

This paper investigates a one-dimensional lattice model of SU(2)_{4} anyons, deriving an effective Hamiltonian and analyzing the structure of the Hilbert space to understand the topological phases and strongly correlated non-Abelian anyons.

Contribution

It introduces an effective low-energy Hamiltonian for SU(2)_{4} anyons and studies the Hilbert space properties within the modular tensor category framework.

Findings

Identified a transition into a topological ordered phase.

Derived an effective Hamiltonian for strongly correlated SU(2)_4 anyons.

Analyzed the Hilbert space structure of the model.

Abstract

One-dimensional lattice model of SU(2)_{4} anyons containing a transition into the topological ordered phase state is considered. An effective low-energy Hamiltonian is found for half-integer and integer indices of the type of strongly correlated non-Abelian anyons. The Hilbert state space properties in the considered modular tensor category are studied.