Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap

We show that recent results on adiabatic theory for interacting gapped many-body systems finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem automorphism group describing infinite volume dynamics quasi-local algebra of observables. The key assumption is existence sequence Hamiltonians, which generates same Our also holds certain perturbations ground states close spectral gap (so it an resonances and, this sense, “generalized”), and provides approximation to all orders parameter (a property often called “super-adiabatic”). In addition existing lattices, perform resummation expansion allow observables are not strictly local. Finally, as application, validity linear higher order response our class systems. While consider result its proof new interesting itself, lay foundation with only bulk, will be presented follow-up article.