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Journal of Physics A Mathematical and Theoretical

Bethe ansatz solution to integrable bosonic cube networks

Lachlan Allan Bennett, Phillip S. Isaac, Jon Links

Published May 13, 2026• 0 citations
Publisher

Abstract

Abstract We study two extended Bose–Hubbard-type Hamiltonians representing bosonic networks restricted to the graph of a cube. For both Hamiltonians, we demonstrate that Bethe ansatz methods of solution can be employed after applying a canonical transformation of operators. We provide the resulting Bethe ansatz equations, and corresponding formulae for states and energies of both Hamiltonians.

DOI
10.1088/1751-8121/ae6d54

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Abstract We study two extended Bose–Hubbard-type Hamiltonians representing bosonic networks restricted to the graph of a cube. For both Hamiltonians, we demonstrate that Bethe ansatz methods of solution can be employed after applying a canonical transformation of operators. We provide the resulting Bethe ansatz equations, and corresponding formulae for states and energies of both Hamiltonians.
I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the gl(2)gl(2)gl(2)-invariant RRR-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a SN−1S^{N-1}SN−1 sphere, where NNN is the total number of atoms in the condensate.