sl(M+1) Construction of Quasi-solvable Quantum M-body Systems
Abstract
We propose a systematic method to construct quasi-solvable quantum many-body systems having permutation symmetry. By the introduction of elementary symmetric polynomials and suitable choice of a solvable sector, the algebraic structure of sl(M+1) naturally emerges. The procedure to solve the canonical-form condition for the two-body problem is presented in detail. It is shown that the resulting two-body quasi-solvable model can be uniquely generalized to the M-body system for arbitrary M under the consideration of the GL(2,K) symmetry. An intimate relation between quantum solvability and supersymmetry is found. With the aid of the GL(2,K) symmetry, we classify the obtained quasi-solvable quantum many-body systems. It turns out that there are essentially five inequivalent models of Inozemtsev type. Furthermore, we discuss the possibility of including M-body (M>=3) interaction terms without destroying the quasi-solvability.
Keywords
Cite
@article{arxiv.hep-th/0306174,
title = {sl(M+1) Construction of Quasi-solvable Quantum M-body Systems},
author = {Toshiaki Tanaka},
journal= {arXiv preprint arXiv:hep-th/0306174},
year = {2014}
}
Comments
41 pages, REVTeX4; (v2) published version; (v3) typos corrected