On non-stationary Lam\'e equation from WZW model and spin-1/2 XYZ chain
Abstract
We study the link between WZW model and the spin-1/2 XYZ chain. This is achieved by comparing the second-order differential equations from them. In the former case, the equation is the Ward-Takahashi identity satisfied by one-point toric conformal blocks. In the latter case, it arises from Baxter's TQ relation. We find that the dimension of the representation space w.r.t. the V-valued primary field in these conformal blocks gets mapped to the total number of chain sites. By doing so, Stroganov's "The Importance of being Odd" (cond-mat/0012035) can be consistently understood in terms of WZW model language. We first confirm this correspondence by taking a trigonometric limit of the XYZ chain. That eigenstates of the resultant two-body Sutherland model from Baxter's TQ relation can be obtained by deforming toric conformal blocks supports our proposal.
Keywords
Cite
@article{arxiv.1202.1764,
title = {On non-stationary Lam\'e equation from WZW model and spin-1/2 XYZ chain},
author = {Ta-Sheng Tai and Reiji Yoshioka},
journal= {arXiv preprint arXiv:1202.1764},
year = {2012}
}
Comments
17 pages, 3 figures; v2: minor revision; v3: typos in equations corrected