Operator Quantum Geometric Tensor and Quantum Phase Transitions
arXiv:1008.0321 · doi:10.1209/0295-5075/91/30003
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.
One more reference added. 6 pages,2 figs. Accepted by EPL
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- Quantum geometric tensor away from Equilibrium
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- Characterizing the Many Body Localization Crossover as a Metal-Insulator Transition: Localization length from Polarization and Quantum Metric