Modular invariance in the gapped XYZ spin-1/2 chain
Name
Ercolessi-2013-Modular invariance in the gapped.pdf
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2.34 MB
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Author(s)
Ercolessi, Elisa
Evangelisti, Stefano
Franchini, Fabio
Ravanini, Francesco
Date Issued
September 2013
Journal
Physical Review B
Publisher
American Physical Society
Citation
Ercolessi, Elisa, Stefano Evangelisti, Fabio Franchini, and Francesco Ravanini. "Modular invariance in the gapped XYZ spin-1/2 chain." Phys. Rev. B 88, 104418 (September 2013). © 2013 American Physical Society
Version
Final published version
Abstract
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 12 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. The encoding of the symmetries of the model into the modular properties of the partition function could shed light on the general structure of integrable models.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.88.104418
