2010/03/31 by Yu-Quan Ma, Shu Chen, Heng Fan +1 · 3 citations
Mathematics · Physics and Astronomy · #Berry connection and curvature #Geometric phase #Mathematics #Physics #Quantum #Quantum and electron transport phenomena #Quantum dynamics #Quantum geometry #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Quantum phases #Quantum process #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.81.245129
published as Phys. Rev. B 81, 245129 (2010) · 5 pages, 2 figures
openalex publication_date 2010/06/29 · arxiv created 2010/07/08 · arxiv updated 2010/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 in 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.