# Timescale for adiabaticity breakdown in driven many-body systems and orthogonality catastrophe. (arXiv:1611.00663v2 [cond-mat.quant-gas] UPDATED)

The adiabatic theorem is a fundamental result established in the early days

of quantum mechanics, which states that a system can be kept arbitrarily close

to the instantaneous ground state of its Hamiltonian if the latter varies in

time slowly enough. The theorem has an impressive record of applications

ranging from foundations of quantum field theory to computational recipes in

molecular dynamics. In light of this success it is remarkable that a

practicable quantitative understanding of what "slowly enough" means is limited

to a modest set of systems mostly having a small Hilbert space. Here we show

how this gap can be bridged for a broad natural class of physical systems,

namely many-body systems where a small move in the parameter space induces an

orthogonality catastrophe. In this class, the conditions for adiabaticity are

derived from the scaling properties of the parameter dependent ground state

without a reference to the excitation spectrum. This finding constitutes a

major simplification of a complex problem, which otherwise requires solving

non-autonomous time evolution in a large Hilbert space. We illustrate our

general results on two examples motivated by recent experiments on Thouless

pumping and on the dynamics of an impurity in a degenerate quantum fluid.