The Yang-Baxter integrability of the critical Ising chain

Abstract

We show that the one dimensional, critical transverse field Ising model is Yang-Baxter integrable. This is done by constructing commuting transfer matrices built out of a $R$-matrix satisfying the Yang-Baxter equation with additive spectral parameters. The $R$-matrix is non-local, as it is expressed in terms of Majorana fermions. It is also non-regular. Nevertheless, we show that the quantum inverse scattering method can still be suitably adapted. We then recursively obtain the conserved quantities [in the infinite volume] by the boost operator method. Remarkably, among the conserved charges we also find the Kramers-Wannier duality and other non-invertible symmetries for the periodic transverse field Ising model.

arXiv commentv3 closer to the published version 29 pages + appendices + references

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Cited by in corpus (3)

• Isolated zero mode in a quantum computer from a duality twist
• Noninvertible Kramers-Wannier duality symmetries for the discrete-time quantum Ising chain
• Almost local integrable models from supersymmetry algebras