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This paper advances the theoretical understanding of non-Hermitian bosonic lattice systems by deriving a unified framework for local conserved quantities in models with quartic and higher-order interactions. By demonstrating that these quantities form a mutually commuting family, the work clarifies integrability conditions in complex many-body settings where traditional Yang-Baxter structures are absent. Such rigorous mathematical foundations are essential for predicting long-time dynamics and thermalization behavior in next-generation quantum simulators and non-Hermitian quantum devices.
Conserved quantities in a bosonic tight-binding chain with non-Hermitian quartic terms
arXiv:2609.14556v1 Announce Type: cross Abstract: We investigate local conserved quantities in non-Hermitian bosonic lattice systems whose underlying Yang--Baxter structure remains unclear. Focusing on a one-dimensional bosonic chain with quartic interactions of creation operators, we provide a new representation of the local conserved quantities previously constructed by Sanatani and Shiraishi. Using Fourier transformation and trigonometric identities, we systematically derive these conserved quantities and show directly that they form a mutually commuting family. We further extend the construction to interactions extending beyond a single site, cubic interactions, asymmetric hopping, and an on-site potential. Our results provide a unified framework for constructing and characterizing local conserved quantities in this class of non-Hermitian many-body systems.
Abstract:We investigate local conserved quantities in non-Hermitian bosonic lattice systems whose underlying Yang--Baxter structure remains unclear. Focusing on a one-dimensional bosonic chain with quartic interactions of creation operators, we provide a new representation of the local conserved quantities previously constructed by Sanatani and Shiraishi. Using Fourier transformation and trigonometric identities, we systematically derive these conserved quantities and show directly that they form a mutually commuting family. We further extend the construction to interactions extending beyond a single site, cubic interactions, asymmetric hopping, and an on-site potential. Our results provide a unified framework for constructing and characterizing local conserved quantities in this class of non-Hermitian many-body systems.
Statistical Mechanics (cond-mat.stat-mech); Quantum Gases (cond-mat.quant-gas); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI); Quantum Physics (quant-ph)
arXiv:2609.14556 [cond-mat.stat-mech]
(or arXiv:2609.14556v1 [cond-mat.stat-mech] for this version)
https://doi.org/10.48550/arXiv.2609.14556 arXiv-issued DOI via DataCite (pending registration)
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