New derivation of the geometric phase

A -K Pati

We use a gauge-invariant 'reference section' and define the geometric phase for all quantum evolutions in a closed form. This geometric phase is obtained by integrating the inner product of the 'reference section' and its path derivative along the evolution curve which is valid for non-cyclic, non-unitary and non-Schrodinger evolutions of quantum systems. Two non-trivial examples are studied to realize our new expression.

Arno Böhm, Luis J. Boya, Brian K. Kendrick

Harald Grosse, W. L. Kennedy

Ole Andersson, Hoshang Heydari

We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann's standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the 'interferometric' geometric phase of Sjöqvist et al (2000 Phys. Rev. Lett. 85 2845–9 ), and for more generally evolving open systems it gives rise to the generalization of the interferometric geometric phase due to Tong et al (2004 Phys. Rev. Lett. 93 080405 ).

E. C. G. Sudarshan, J. Anandan, T. R. Govindarajan

Shan Chuan-Jia

In this paper, we diagonalize the Hamiltonian of the one-dimensional spin chain system with three-body interaction. Then we solve geometric phase of ground state in the system through a rotating operation. By the numerical calculation of the geometric phase and its derivative, we consider the three-body interaction effects on the geometric phase and quantum phase transition, the results show that the geometric phase can be well used to characterize quantum phase transition in this system, and find that three-body interaction not only can move the criticality region, but also can generate a new critical point.