Quantum covariant derivative
Quantum Physics
2023-11-03 v4 Other Condensed Matter
Abstract
The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate transformations and compatible with the quantum geometric tensor. The quantum covariant derivative is used to derive a gauge- and coordinate-invariant adiabatic perturbation theory, providing an efficient tool for calculations of nonlinear adiabatic response properties.
Cite
@article{arxiv.2206.01716,
title = {Quantum covariant derivative},
author = {Ryan Requist},
journal= {arXiv preprint arXiv:2206.01716},
year = {2023}
}