A Quantized Inter-level Character in Quantum Systems

Abstract

For a quantum system subject to external parameters, the Berry phase is an intra-level property, which is gauge invariant module $2\pi$ for a closed loop in the parameter space and generally is non-quantized. In contrast, we define a inter-band character $\Theta$ for a closed loop, which is gauge invariant and quantized as integer values. It is a quantum mechanical analogy of the Euler character based on the Gauss-Bonnet theorem for a manifold with a boundary. The role of the Gaussian curvature is mimicked by the difference between the Berry curvatures of the two levels, and the counterpart of the geodesic curvature is the quantum geometric potential which was proposed to improve the quantum adiabatic condition. This quantized inter-band character is also generalized to quantum degenerate systems.

References in corpus (10)

• Dissipationless Quantum Spin Current at Room Temperature
• Adiabatic Quantum Computing
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Cited by in corpus (8)

• Nonreciprocal Landau-Zener tunneling
• Nonadiabatic Nonlinear Optics and Quantum Geometry -- Application to the Twisted Schwinger Effect
• A Quantized Interband Topological Index in Two-Dimensional Systems
• Berry connection and quantum geometry in time-dependent systems with instantaneous quantum integrable field theory
• Demonstration of geometric diabatic control of quantum states
• Multi-tunneling effect of nonreciprocal Landau-Zener tunneling: Insights from DC field responses
• Geometric Effects on Tunneling in Driven Quantum Systems
• Gauge-invariant optical selection rules for excitons