On non-stationary Lamé equation from WZW model and spin-1/2 XYZ chain

Details On non-stationary Lamé equation from WZW model and spin-1/2 XYZ chain On non-stationary Lamé equation from WZW model and spin-1/2 XYZ chain

2012-02-08

arxiv.org/abs/1202.1764v3

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, 3 figures; v2: minor revision; v3: typos in equations corrected

Scientific paper

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.

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