Geometric phase

Summary

The geometric phase, or Berry phase, is a phase acquired by an eigenstate of a quantum Hamiltonian. It appears when the parameters of the Hamiltonian are moved slowly around a closed loop, in addition to the usual dynamical phase. It depends only on the loop in parameter space, not on the speed at which it is traversed. Mathematically it is the holonomy of a natural connection, the Berry connection, on the line bundle of eigenvectors. It explains effects such as the Aharonov–Bohm effect and the quantisation of the Hall conductance, and its optical case is the Pancharatnam–Berry phase.