Bound states in string nets

TL;DR

This paper investigates the formation and properties of bound states in string-net models under string tension, revealing how their number and energy depend on the quantum dimension and lattice geometry.

Contribution

It provides a detailed analysis of bound states in string-net Hamiltonians, including their emergence, energy calculations, and structural properties across different lattice geometries.

Findings

Bound states appear in ladder geometries with finite or zero tension.

Binding energy depends on the total quantum dimension.

Number of bound states in honeycomb lattice varies with quantum dimension.

Abstract

We discuss the emergence of bound states in the low-energy spectrum of the string-net Hamiltonian in the presence of a string tension. In the ladder geometry, we show that a single bound state arises either for a finite tension or in the zero-tension limit depending on the theory considered. In the latter case, we perturbatively compute the binding energy as a function of the total quantum dimension. We also address this issue in the honeycomb lattice where the number of bound states in the topological phase depends on the total quantum dimension. Finally, the internal structure of these bound states is analyzed in the zero-tension limit.