Effects of Ill-Defined Domain of Definitions of the Parameter Operator on Berry Curvature and the Adiabatic Theorem

2025/07/28 by Konstantinou, Georgios, Moulopoulos, Konstantinos
#FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2507.20679

Abstract

We present a comprehensive analytical study that extends the conventional formulation of Berry curvature, highlighting its derivation in the context of problematic domains of definition of the operators. Our analysis reveals that handling these domains carefully can have a substantial impact on Berry curvature, demonstrating that even Hamiltonians without explicit parameter dependence may exhibit nonzero Berry curvature. This finding emphasizes that Berry curvature is intrinsically related to the eigenvectors rather than the Hamiltonian itself. Our approach utilizes the standard Bloch (k-space) framework for spatially periodic systems, illustrating these effects from first principles and discussing potential implications for solid-state systems.

Citations

• Topological anomalies in the off-diagonal Ehrenfest theorem and their role on optical transitions in solar cells
• Emergent non-Hermitian contributions to the Ehrenfest and Hellmann-Feynman theorems
• Quantal phase factors accompanying adiabatic changes

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