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arXiv · 2603.10972

Violating the All-or-Nothing Picture of Local Charges in Non-Hermitian Bosonic Chains

Mizuki Sanatani·Naoto Shiraishi
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Abstract

We present explicit counterexamples to a widespread empirical expectation that local commuting charges display all-or-nothing behavior. In the class of bosonic chains with symmetric nearest-neighbor hopping and arbitrary on-site terms (including non-Hermitian terms), we exhibit systems that possess k-local charges for some but not all k. Concretely, we construct non-Hermitian models with a 3-local charge but no other nontrivial local charges and models with k-local charges for all k except k = 4. These results show that the Grabowski--Mathieu integrability test based on 3-local charges is not universally applicable. We further give necessary and sufficient conditions for the existence of k-local charges in this class, yielding an exhaustive classification and uncovering additional integrable models.

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Mizuki Sanatani, Naoto Shiraishi. 2026-03-11. Violating the All-or-Nothing Picture of Local Charges in Non-Hermitian Bosonic Chains. https://arxiv.org/abs/2603.10972

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