Is there a model of the 1D Bose gas (aka the Lieb Liniger Model) on a lattice that retains integrability? As a naive guess, I had thought that the Bose Hubbard model would fit this criterion, since the Fermi Hubbard model is integrable (although I would guess the constraints imposed by the Pauli exclusion principle are important in ensuring integrability). Is this line of reasoning correct? Why or why not?
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