Modular invariance in the gapped XYZ spin 1/2 chain

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.

17 pages, 4 figures, 1 table. Accepted published version

References in corpus (4)

• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain
• Corrections to scaling for block entanglement in massive spin-chains
• Correlation Length and Unusual Corrections to the Entanglement Entropy

Cited by in corpus (12)

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• Negativity spectrum in 1D gapped phases of matter
• The Frustration of being Odd: How Boundary Conditions can destroy Local Order
• Entanglement Entropy from Corner Transfer Matrix in Forrester Baxter non-unitary RSOS models
• On the Möbius transformation in the entanglement entropy of fermionic chains
• Exact dimer phase with anisotropic interaction for one dimensional magnets
• Quantum magnetism with ultracold bosons carrying orbital angular momentum
• Exact phase diagram and topological phase transitions of the XYZ spin chain
• Emergence of Gaussianity in the thermodynamic limit of interacting fermions