Thursday, February 9, 2012

1202.1764 (Kohei Motegi et al.)

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

Kohei Motegi, Ta-Sheng Tai, Reiji Yoshioka
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 what is satisfied by one-point toric conformal
blocks. In the latter, it arises from Baxter's TQ relation. We find the
dimension of the representation space of 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 further confirm this
correspondence by taking a trigonometric limit of the XYZ chain. That
eigenstates of the resultant two-body Sutherland model can be obtained from
deformed toric conformal blocks supports our proposal.
View original: http://arxiv.org/abs/1202.1764

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