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arXiv · 2601.11806

Any local Hamiltonian with ferromagnetic quantum many-body scars has a generalized Shiraishi-Mori form

Keita Omiya
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Abstract

Quantum many-body scars (QMBS) are nonthermal eigenstates embedded in otherwise thermal spectra. A broad class of exact QMBS is realized as fixed-momentum magnon states above a ferromagnetic reference state. Here we prove a structural theorem for this class. Specifically, we show that any local Hamiltonian hosting such ``ferromagnetic scar states'' necessarily admits a decomposition into a Zeeman term and terms containing local projectors that annihilate the scar states locally. This result establishes that an appropriate generalization of the Shiraishi--Mori construction is essentially exhaustive for ferromagnetic QMBS and provides a unified structural explanation for the recurrent appearance of projector-based interactions and equally spaced scar towers across a broad family of exact scar Hamiltonians.

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Keita Omiya. 2026-01-16. Any local Hamiltonian with ferromagnetic quantum many-body scars has a generalized Shiraishi-Mori form. https://arxiv.org/abs/2601.11806

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