Abelian and Non-Abelian Quantum Geometric Tensor

Details Abelian and Non-Abelian Quantum Geometric Tensor Abelian and Non-Abelian Quantum Geometric Tensor

2010-03-22

arxiv.org/abs/1003.4040v3

Phys. Rev. B 81, 245129 (2010)

Physics

Quantum Physics

5 pages, 2 figures

Scientific paper

10.1103/PhysRevB.81.245129

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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