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

TL;DR

This paper introduces a class of integrable bosonic networks based on bipartite graphs, demonstrating their Yang-Baxter integrability and deriving conserved operators via the classical Yang-Baxter equation.

Contribution

It constructs a new class of quantum Hamiltonians for bosonic networks that are proven to be Yang-Baxter integrable, with explicit conserved operators derived from classical solutions.

Findings

Quantum Hamiltonians are Yang-Baxter integrable.

Conserved operators are explicitly constructed.

Applications of integrability are discussed.

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.