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Bethe Ansatz solution for a model of global-range interacting bosons on the square lattice

Quantum systems on a one-dimensional lattice are ubiquitous in the study of models exactly-solved by Bethe Ansatz techniques. Here it is shown that including global-range interaction opens scope for Bethe Ansatz solutions that are not constrained to one-dimensional quantum systems. A bosonic model on a square lattice is defined, and the exact Bethe Ansatz solution is provided for open, cylindrical, and toroidal boundary conditions. Generalising the result for an integrable defect leads to a Bethe Ansatz solution that is not expressible in an exact, closed-form manner.

preprint2025arXivOpen access
Jon Links
nlin.SI
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