Bounds on quantum adiabaticity in driven many-body systems from generalized orthogonality catastrophe and quantum speed limit

TL;DR

This paper derives new inequalities to estimate adiabatic fidelity in driven many-body quantum systems, utilizing generalized orthogonality catastrophe and quantum speed limit, with improved bounds demonstrated on a Rice-Mele model.

Contribution

It introduces stronger bounds on adiabatic fidelity using a two-dimensional subspace approach, applicable to broad classes of quantum many-body systems.

Findings

Derived nearly sharp bounds for large systems

Applied bounds to driven Rice-Mele model

Demonstrated improved estimates over previous methods

Abstract

We provide two inequalities for estimating adiabatic fidelity in terms of two other more handily calculated quantities, i.e., generalized orthogonality catastrophe and quantum speed limit. As a result of considering a two-dimensional subspace spanned by the initial ground state and its orthogonal complement, our method leads to stronger bounds on adiabatic fidelity than those previously obtained. One of the two inequalities is nearly sharp when the system size is large, as illustrated using a driven Rice-Mele model, which represents a broad class of quantum many-body systems whose overlap of different instantaneous ground states exhibits orthogonality catastrophe.