Quantum adiabaticity in many-body systems and almost-orthogonality in complementary subspace

TL;DR

This paper explains why adiabatic fidelity and ground state overlap are nearly identical in many-body systems, attributing it to the limits of small evolution parameters and large system sizes, supported by two model examples.

Contribution

It introduces a unified explanation for the near-orthogonality phenomenon in many-body systems based on system size and evolution parameters.

Findings

Adiabatic fidelity and ground state overlap are nearly identical due to system size effects.

Pairs of vectors orthogonal to the initial state tend to become nearly orthogonal as system size increases.

Theoretical insights are demonstrated with driven Rice-Mele and Kitaev chain models.

Abstract

We investigate why, in quantum many-body systems, the adiabatic fidelity and the overlap between the initial state and instantaneous ground states often yield nearly identical values. Our analysis suggests that this phenomenon results from an interplay between two intrinsic limits of many-body systems: the limit of small evolution parameters and the limit of large system sizes. In the former case, conventional perturbation theory provides a straightforward explanation. In the latter case, a key insight is that pairs of vectors in the Hilbert space orthogonal to the initial state tend to become nearly orthogonal as the system size increases. We illustrate these general findings with two representative models of driven many-body systems: the driven Rice-Mele model and the driven interacting Kitaev chain model.