Operator quantum geometric tensor and quantum phase transitions

Xiao-Ming Lu^a and Xiaoguang Wang^b

Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University - Hangzhou 310027, PRC

^a luxiaoming@gmail.com
^b xgwang@zimp.zju.edu.cn

Received: 10 March 2010
Accepted: 31 July 2010

Abstract

We extend the quantum geometric tensor from the state space to the operator level, and investigate its properties like the additivity for factorizable models and the splitting of two kinds contributions for the case of stationary reference states. This operator quantum geometric tensor (OQGT) is shown to reflect the sensitivity of unitary operations against perturbations of multi-parameters. General results for the cases of time evolutions with given stationary reference states are obtained. By this approach, we get exact results for the rotated XY models, and show relations between the OQGT and quantum criticality.