Supersymmetric quantum spin chains and classical integrable systems
Abstract
For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of generating function for the family of commuting quantum transfer matrices. Any eigenvalue of the master T-operator is the tau-function of the classical mKP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0-th time of the hierarchy. This implies a remarkable relation between the quantum supersymmetric spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, we obtain a system of algebraic equations for the spectrum of the spin chain Hamiltonians.
Cite
@article{arxiv.1412.2586,
title = {Supersymmetric quantum spin chains and classical integrable systems},
author = {Zengo Tsuboi and Anton Zabrodin and Andrei Zotov},
journal= {arXiv preprint arXiv:1412.2586},
year = {2015}
}
Comments
44 pages, v2: minor corrections