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

Quantum Physics [Submitted on 16 Mar 2026] Role of spectral structure in adiabatic ground-state preparation of the XXZ model Francisco Albarrán-Arriagada, Juan Carlos Retamal 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. Comments: 8 pages, 5 Figures, 2 Tables Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Cite as: arXiv:2603.15794 [quant-ph]   (or arXiv:2603.15794v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.15794 Focus to learn more Submission history From: Francisco Damaso Albarrán-Arriagada Ph.D [view email] [v1] Mon, 16 Mar 2026 18:25:22 UTC (778 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.mes-hall References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)