Conserved quantities in a bosonic tight-binding chain with non-Hermitian quartic terms

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.