Operator Quantum Geometric Tensor and Quantum Phase Transitions

TL;DR

This paper introduces the operator quantum geometric tensor (OQGT), extending the quantum geometric tensor to the operator level, and demonstrates its effectiveness in analyzing quantum phase transitions and criticality.

Contribution

It develops the theory of OQGT, explores its properties, and applies it to exactly analyze quantum criticality in rotated XY models.

Findings

OQGT reflects the sensitivity of unitary operations to parameter perturbations

Exact results for rotated XY models are obtained using OQGT

Relations between OQGT and quantum criticality are established

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.