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

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.15238
 arXiv:
 arXiv:2012.15238
 Bibcode:
 2020arXiv201215238H
 Keywords:

 Mathematical Physics;
 Quantum Physics;
 81Q15;
 81Q20;
 81V70
 EPrint:
 V1 >