Exact few-magnon Bethe scars of the non-integrable alternating Heisenberg chain

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 coordinate 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. These states exhibit wavefunction scarring similar to that of single-particle states in chaotic billiards. We discuss a general numerical recipe to diagnose the existence of such generalized Bethe ansatz (GBA) scar states and also provide exact analytic expressions for their entanglement. 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.

23 pages, 9 figures, 4 tables, 3 appendices. Title changed. v2 closely matches version accepted by Phys. Rev. B

Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

arXiv:2501.14017 [cond-mat.str-el]

(or arXiv:2501.14017v2 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2501.14017 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1103/2g33-l3y6 Focus to learn more DOI(s) linking to related resources

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