2016/11/30 by Wei Chen, Markus Legner, Andreas Rüegg +1
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Critical exponent #Geometry #Mathematics #Phase transition #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Renormalization group #Scaling #Symmetry protected topological order #Topological Materials and Phenomena #Topological insulator #Topological order #Topology (electrical circuits) #Universality (dynamical systems) #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.95.075116
published as Phys. Rev. B 95, 075116 (2017) · 13 pages, 7 figures
arxiv created 2017/02/07 · openalex publication_date 2017/02/07 · arxiv updated 2017/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by 2\ifmmode×\else\texttimes\fi2 Dirac Hamiltonians are discussed. In one dimension, the correlation function measures the charge-polarization correlation between Wannier states at different positions, while in two dimensions it measures the itinerant-circulation correlation between Wannier states. The correlation function is nonzero in both the topologically trivial and nontrivial states, and allows us to extract a correlation length that diverges at topological phase transitions. The correlation length and the curvature function that defines the topological invariants are shown to have universal critical exponents, allowing the notion of universality classes to be introduced. Particularly in two dimensions, the universality class is determined by the orbital symmetry of the Dirac model. The scaling laws that constrain the critical exponents are revealed, and are predicted to be satisfied even in interacting systems, as demonstrated in an interacting topological Kondo insulator.