Exact eigenstates for contact interactions
Abstract
Description
We show that in d>1 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-1/2 XXZ Heisenberg models.
23 pages. More references, enlarged introduction, remark 2.9 corrected. To appear in Journal of Statistical Physics
23 pages. More references, enlarged introduction, remark 2.9 corrected. To appear in Journal of Statistical Physics