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

TL;DR

This paper derives a universal scaling law for the breakdown of adiabaticity in many-body quantum systems experiencing an orthogonality catastrophe, simplifying the understanding of adiabatic limits without detailed spectral analysis.

Contribution

It introduces a broad class of many-body systems where adiabaticity conditions depend on ground state scaling, bypassing complex spectral calculations.

Findings

Derived a scaling law for adiabaticity breakdown in many-body systems.

Linked adiabaticity conditions to ground state properties rather than excitation spectra.

Applied results to analyze transport quantization in topological pumps.

Abstract

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 by analyzing conditions for the transport quantization in a topological Thouless pump.