Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''

TL;DR

This supplementary paper provides detailed derivations, additional examples, and analysis of the scaling behavior and long-time dynamics of correlation functions in low-dimensional gapless systems, focusing on nonintegrable models like the Bose-Hubbard model.

Contribution

It offers detailed derivations, additional examples, and analysis of the effects of nonintegrability on the dynamics of correlation functions in low-dimensional systems.

Findings

Scaling behavior of correlation functions analyzed

Effects of nonintegrability on long-time dynamics studied

Classification of slow dynamics regimes provided

Abstract

Here we give detailed derivations and provide additional examples to the main paper: arXiv:0706.0212. In particular, we discuss the scaling behavior of observables like correlation functions and density of excitations. We also analyze effects of nonintegrability of the Bose-Hubbard model on the long-time dynamics of the correlation functions. In addition we explicitly consider several interacting models, where we are able to analyze slow dynamics and classify it according to the regimes suggested in the main paper.