Violating the All-or-Nothing Picture of Local Charges in Non-Hermitian Bosonic Chains
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908969314811904 |
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| author | Yamaguchi, Mizuki Shiraishi, Naoto |
| author_facet | Yamaguchi, Mizuki Shiraishi, Naoto |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_10972 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Violating the All-or-Nothing Picture of Local Charges in Non-Hermitian Bosonic Chains Yamaguchi, Mizuki Shiraishi, Naoto Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics 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. |
| title | Violating the All-or-Nothing Picture of Local Charges in Non-Hermitian Bosonic Chains |
| topic | Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics |
| url | https://arxiv.org/abs/2603.10972 |