The Yang-Baxter integrability of the critical Ising chain

TL;DR

This paper demonstrates that the critical transverse field Ising model in one dimension is integrable via the Yang-Baxter framework, using a non-local, non-regular R-matrix constructed from Majorana fermions, and extends the quantum inverse scattering method to this context.

Contribution

It constructs a Yang-Baxter integrable structure for the critical Ising chain with a novel non-local, non-regular R-matrix and adapts the quantum inverse scattering method accordingly.

Findings

Identifies a non-local, non-regular R-matrix satisfying the Yang-Baxter equation.

Recursively derives conserved quantities including duality and non-invertible symmetries.

Shows the applicability of the quantum inverse scattering method to this integrable model.

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.