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arXiv:2507.00483 · Journal of Geometry and Physics

Explicit conserved operators for a class of integrable bosonic networks from the classical Yang-Baxter equation

Phillip S. Isaac, Jon Links, Inna Lukyanenko, Jason L. Werry

Published Apr 7, 2026• 1 citation
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Abstract

Let B denote the weighted adjacency matrix of a balanced, symmetric, bipartite graph. We define a class of bosonic networks given by Hamiltonians whose hopping terms are determined by B . We show that each quantum Hamiltonian is Yang-Baxter integrable, admitting a set of mutually commuting operators derived through a solution of the classical Yang-Baxter equation. We discuss some applications and consequences of this result.

DOI
10.1016/j.geomphys.2026.105837

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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.
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