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Abstract: We propose a generalized quantum geometric tenor to understand topologicalquantum phase transitions, which can be defined on the parameter space with theadiabatic evolution of a quantum many-body system. The generalized quantumgeometric tenor contains two different local measurements, the non-AbelianRiemannian metric and the non-Abelian Berry curvature, which are recognized astwo natural geometric characterizations for the change of the ground-stateproperties when the parameter of the Hamiltonian varies. Our results show thesymmetry-breaking and topological quantum phase transitions can be understoodas the singular behavior of the local and topological properties of the quantumgeometric tenor in the thermodynamic limit.

Autor: Yu-Quan Ma, Shu Chen, Heng Fan, Wu-Ming Liu

Fuente: https://arxiv.org/

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