Abelian and non-Abelian quantum geometric tensor

Yu-Quan Ma, Shu Chen, Heng Fan, Wu-Ming Liu
2010 Physical Review B  
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
more » ... ltonian 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.
doi:10.1103/physrevb.81.245129 fatcat:ecmkx66b7vb4tkst6pyzmzlzoe