1301.6758 (Elisa Ercolessi et al.)

Modular invariance in the gapped XYZ spin chain    [PDF]

Elisa Ercolessi, Stefano Evangelisti, Fabio Franchini, Francesco Ravanini

We show that the elliptic parametrization of the coupling constants of the quantum XYZ spin chain can be analytically extended outside of their natural domain, to cover the whole phase-diagram of the model, which is composed of twelve adjacent regions, related to one another by a spin rotation. This extension is based on the modular properties of the elliptic functions and we show how rotations in parameter space correspond to the double covering PGL(2,Z) of the modular group, implying that the partition function of the XYZ chain is invariant under this group in parameter space, in the same way as a Conformal Field Theory partition function is invariant under the modular group acting in real space.

View original: http://arxiv.org/abs/1301.6758