Paper

{
  "raw_xml": "<entry>\n    <id>http://arxiv.org/abs/2603.10972v1</id>\n    <title>Violating the All-or-Nothing Picture of Local Charges in Non-Hermitian Bosonic Chains</title>\n    <updated>2026-03-11T16:57:23Z</updated>\n    <link href='https://arxiv.org/abs/2603.10972v1' rel='alternate' type='text/html'/>\n    <link href='https://arxiv.org/pdf/2603.10972v1' rel='related' title='pdf' type='application/pdf'/>\n    <summary>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.</summary>\n    <category scheme='http://arxiv.org/schemas/atom' term='cond-mat.stat-mech'/>\n    <category scheme='http://arxiv.org/schemas/atom' term='math-ph'/>\n    <category scheme='http://arxiv.org/schemas/atom' term='nlin.SI'/>\n    <category scheme='http://arxiv.org/schemas/atom' term='quant-ph'/>\n    <published>2026-03-11T16:57:23Z</published>\n    <arxiv:comment>42 pages, no figures</arxiv:comment>\n    <arxiv:primary_category term='cond-mat.stat-mech'/>\n    <author>\n      <name>Mizuki Yamaguchi</name>\n    </author>\n    <author>\n      <name>Naoto Shiraishi</name>\n    </author>\n  </entry>"
}