Non-invertible Kramers-Wannier duality-symmetry in the trotterized critical Ising chain

Integrable trotterization provides a method to evolve a continuous time integrable many-body system in discrete time, such that it retains its conserved quantities. Here we explicitly show that the first order trotterization of the critical transverse field Ising model is integrable. The discrete time conserved quantities are obtained from an inhomogeneous transfer matrix constructed using the quantum inverse scattering method. The inhomogeneity parameter determines the discrete time step. We then focus on the non-invertible Kramers-Wannier duality-symmetry for the trotterized evolution. We find that the discretization of both space and time leads to a doubling of these duality operators. They account for discrete translations in both space and time. As an interesting application, we find that these operators also provide maps between trotterizations of different orders. This helps us extend our results beyond the trotterization scheme and investigate the Kramers-Wannier duality-symmetry for finite time Floquet evolution of the critical transverse field Ising chain.