Role of spectral structure in adiabatic ground-state preparation of the XXZ model

TL;DR

This paper investigates how the spectral structure of the XXZ model affects adiabatic ground-state preparation, highlighting the importance of spectral engineering to overcome degeneracies and improve protocol efficiency.

Contribution

It demonstrates that spectral degeneracies limit adiabatic preparation and shows that spectral engineering strategies like initial Hamiltonian optimization significantly enhance performance.

Findings

Spectral degeneracies constrain adiabatic protocols.

Optimization of initial Hamiltonian suppresses level crossings.

Counterdiabatic driving is effective only after removing degeneracies.

Abstract

Adiabatic ground-state preparation is fundamentally limited by the spectral structure of the time-dependent Hamiltonian, particularly by gap reductions and degeneracies that induce nonadiabatic transitions. We examine this dependence in the anisotropic Heisenberg (XXZ) model on an eight-site ring by comparing three strategies: optimization of the initial Hamiltonian, addition of auxiliary terms, and considering approximate counterdiabatic driving. Owing to anisotropy-dependent level crossings among low-energy states, the XXZ model provides a stringent benchmark. We find that performance is mainly constrained by spectral degeneracies between the ground and excited states. Simple strategies such as initial-Hamiltonian optimization or site-dependent Zeeman fields, suppresses critical crossings and drastically enhance ground-state preparation. In contrast, counterdiabatic terms alone do not improve the protocol when the spectral structure remains level-crossings, becoming effective only after degeneracies are removed. These results identify spectral engineering as a prerequisite for efficient adiabatic ground-state preparation in interacting spin systems.