The Yang-Baxter integrability of the critical Ising chain

2025/06/04 by Sinha, Akash, Justin, Tinu, Padmanabhan, Pramod +1 · 3 citations
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2506.03668

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.

Citations

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Cited by

• Non-invertible Kramers-Wannier duality-symmetry in the trotterized critical Ising chain
• Integrability of a family of clean SYK models from the critical Ising chain
• Almost local integrable models from supersymmetry algebras

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