Incoherent bound states in an infinite $XXZ$ chain at $\Delta=-1/2$

TL;DR

This paper constructs a family of three-magnon states in an infinite $XXZ$ chain at $ ext{Delta}=-1/2$ that are translation-invariant and violate the string conjecture, all sharing the same energy.

Contribution

It introduces a new family of translation-invariant three-magnon states in the $XXZ$ chain that challenge the string conjecture at $ ext{Delta}=-1/2$.

Findings

All constructed states share the same energy.

The states do not satisfy the string conjecture.

The states are translation-invariant.

Abstract

For an infinite $XXZ$ chain with $\Delta=-1/2$ we have obtained a family of translationary invariant three-magnon states which do not satisfy the string conjecture. All of them have the same energy.