The Yang-Baxter integrability of the critical Ising chain

We demonstrate that the one-dimensional critical transverse field Ising model (TFIM) is Yang-Baxter integrable. This is achieved by constructing commuting transfer matrices derived from an R-matrix that satisfies the Yang-Baxter equation with additive spectral parameters. The R-matrix is nonlocal because 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. Using the boost operator method, we recursively obtain the conserved quantities in the infinite volume. Among the conserved charges, we identify the Kramers-Wannier duality and other non-invertible symmetries for the periodic TFIM.