Time scale for adiabaticity breakdown in driven many-body systems and orthogonality catastrophe

Understand

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.