Quantum covariant derivative

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.

References in corpus (9)

• Quantum critical scaling of the geometric tensors
• Band geometry, Berry curvature and superfluid weight
• Geometric phases and criticality in spin chain systems
• Towards high-throughput superconductor discovery via machine learning
• Geometry of quantum phase transitions
• Asymptotic analysis of the Berry curvature in the $E\otimes e$ Jahn-Teller model
• Exact factorization-based density functional theory of electron-phonon systems
• Regularized Born-Oppenheimer molecular dynamics
• Geometric energy transfer in two-component systems

Cited by in corpus (1)

• Quantum geometric tensors from sub-bundle geometry