Exact eigenstates for contact interactions
Statistical Mechanics
2007-05-23 v2 Mathematical Physics
math.MP
Quantum Physics
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/0109538,
title = {Exact eigenstates for contact interactions},
author = {Andras Suto},
journal= {arXiv preprint arXiv:cond-mat/0109538},
year = {2007}
}
Comments
23 pages. More references, enlarged introduction, remark 2.9 corrected. To appear in Journal of Statistical Physics