Abelian and Non-Abelian Quantum Geometric Tensor

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.

5 pages, 2 figures

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Cited by in corpus (6)

• Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
• Steady-state Hall response and quantum geometry of driven-dissipative lattices
• Conventional quantum phase transition driven by complex parameter in non-Hermitian PT-symmetric Ising model
• Geometric Critical Exponents in Classical and Quantum Phase Transitions
• Quantum distance and the Euler number index of the Bloch band in a 1D spin model
• Effective description of Chern insulators