Abstract
We show that in d≥2 dimensions the N-particle kinetic energy operator with periodic boundary conditions has symmetric eigenfunctions which vanish at particle encounters, and give a full description of these functions. In two and three dimensions they represent common eigenstates of bosonic Hamiltonians with any kind of contact interactions, and illustrate a partial “multi-dimensional Bethe Ansatz” or “quantum KAM theorem.” The lattice analogs of these functions exist for N≤L [d/2] where L is the linear size of the box, and are common eigenstates of Bose–Hubbard Hamiltonians and spin-\(\frac{1}{2}\) XXZ Heisenberg models.
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Sütő, A. Exact Eigenstates for Contact Interactions. Journal of Statistical Physics 109, 1051–1072 (2002). https://doi.org/10.1023/A:1020476627111
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DOI: https://doi.org/10.1023/A:1020476627111