Exact eigenstates for contact interactions

Details Exact eigenstates for contact interactions Exact eigenstates for contact interactions

2001-09-28

arxiv.org/abs/cond-mat/0109538v2

J. Stat. Phys. 109 (2002) 1051-1072

Physics

Condensed Matter

Statistical Mechanics

23 pages. More references, enlarged introduction, remark 2.9 corrected. To appear in Journal of Statistical Physics

Scientific paper

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.

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