Exact counterdiabatic driving in finite topological lattice models

Adiabatic protocols are often employed in state preparation schemes but require the system to be driven by a slowly varying Hamiltonian so that transitions between instantaneous eigenstates are exponentially suppressed. Counterdiabatic driving is a technique to speed up adiabatic protocols by including additional terms calculated from the instantaneous eigenstates that counter diabatic excitations. However, this approach requires knowledge of the full eigenspectrum meaning that the exact analytical form of counterdiabatic driving is only known for a subset of problems, e.g., the harmonic oscillator and transverse field Ising model. We extend this subset of problems to include the general family of one-dimensional noninteracting lattice models with open boundary conditions and arbitrary onsite potential, tunneling terms, and lattice size. We will derive a general analytical form for the counterdiabatic term for all states of lattice models, including bound and in-gap states which appear, e.g., in topological insulators. We also derive the general analytical form of targeted counterdiabatic driving terms which are tailored to enforce the dynamical state to remain in a specific state. As an example of the use of the derived analytical forms, we consider state transfer using the topological edge states of the Su-Schrieffer-Heeger model. The derived analytical counterdiabatic driving Hamiltonian can be utilized to inform control protocols in many-body lattice models or to probe the nonequilibrium properties of lattice models.