2001/09/30 by Andras Suto
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #math-ph #math.MP #quant-ph
published as J. Stat. Phys. 109 (2002) 1051-1072 · 23 pages. More references, enlarged introduction, remark 2.9 corrected. To appear in Journal of Statistical Physics
arxiv created 2002/09/17 · arxiv updated 2009/11/30
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.