Exact generalized Bethe eigenstates of the non-integrable alternating Heisenberg chain

TL;DR

This paper demonstrates that the non-integrable alternating Heisenberg chain admits exact solutions for certain eigenstates using a modified Bethe ansatz, revealing hidden structure and zero-energy states.

Contribution

It introduces a generalized Bethe ansatz approach to find exact eigenstates in a non-integrable quantum spin chain, expanding understanding of such systems.

Findings

Existence of exponentially many zero-energy states.

Explicit compact expressions for some eigenstates.

A numerical method to identify generalized Bethe ansatz states.

Abstract

Exact solutions of quantum lattice models serve as useful guides for interpreting physical phenomena in condensed matter systems. Prominent examples of integrability appear in one dimension, including the Heisenberg chain, where the Bethe ansatz method has been widely successful. Recent work has noted that certain non-integrable models harbor quantum many-body scar states, which form a superspin of regular states hidden in an otherwise chaotic spectrum. Here we consider one of the simplest examples of a non-integrable model, the alternating ferromagnetic-antiferromagnetic (bond-staggered) Heisenberg chain, a close cousin of the spin-1 Haldane chain and a spin analog of the Su-Schrieffer-Heeger model, and show the presence of exponentially many zero-energy states. We highlight features of the alternating chain that allow treatment with the Bethe ansatz (with important modifications) and surprisingly for a non-integrable system, we find simple compact expressions for zero-energy eigenfunctions for a few magnons including solutions with fractionalized particle momentum. We discuss a general numerical recipe to diagnose the existence of such generalized Bethe ansatz (GBA) states and also provide exact analytic expressions for the entanglement of such states. We conclude by conjecturing a picture of magnon pairing which may generalize to multiple magnons. Our work opens the avenue to describe certain eigenstates of partially integrable systems using the GBA.