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

TL;DR

This paper demonstrates the integrability of the first order trotterized critical Ising model, explores the non-invertible Kramers-Wannier duality-symmetry in discrete time, and extends the analysis to finite time Floquet evolution.

Contribution

It explicitly constructs discrete time conserved quantities for the trotterized Ising model and reveals how duality operators double and relate different trotterization schemes.

Findings

Trotterization preserves integrability via inhomogeneous transfer matrices.

Duality operators double due to discretization, acting as translations.

Duality maps connect different trotterization orders and finite time evolutions.

Abstract

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.