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arXiv · 1003.4040

Abelian and Non-Abelian Quantum Geometric Tensor

Yu-Quan Ma·Shu Chen·Heng Fan·Wu-Ming Liu
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Abstract

We propose a generalized quantum geometric tenor to understand topological quantum phase transitions, which can be defined on the parameter space with the adiabatic evolution of a quantum many-body system. The generalized quantum geometric tenor contains two different local measurements, the non-Abelian Riemannian metric and the non-Abelian Berry curvature, which are recognized as two natural geometric characterizations for the change of the ground-state properties when the parameter of the Hamiltonian varies. Our results show the symmetry-breaking and topological quantum phase transitions can be understood as the singular behavior of the local and topological properties of the quantum geometric tenor in the thermodynamic limit.

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Yu-Quan Ma, Shu Chen, Heng Fan, Wu-Ming Liu. 2010-03-22. Abelian and Non-Abelian Quantum Geometric Tensor. https://doi.org/10.1103/physrevb.81.245129

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