Universal nonanalytic behavior of the Hall conductance in a Chern insulator at the topologically driven nonequilibrium phase transition

2015/11/30 by Pei Wang, Markus Schmitt, Stefan Kehrein · 34 citations
Physics and Astronomy · #Condensed matter physics #Conductance #Insulator (electricity) #Non-equilibrium thermodynamics #Phase transition #Physics #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #cond-mat.quant-gas #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.93.085134

published in Physical review. B./Physical review. B 93(8) (American Physical Society) · 18 pages, 8 figures

arxiv created 2015/12/05 · openalex publication_date 2016/02/24 · arxiv updated 2017/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the Hall conductance of a Chern insulator after a global quench of the Hamiltonian. The Hall conductance in the long time limit is obtained by applying the linear response theory to the diagonal ensemble. It is expressed as the integral of the Berry curvature weighted by the occupation number over the Brillouin zone. We identify a topologically driven nonequilibrium phase transition, which is indicated by the nonanalyticity of the Hall conductance as a function of the energy gap m_f in the post-quench Hamiltonian \stackrel\ifmmode \else \\fiH_f. The topological invariant for the quenched state is the winding number of the Green's function W, which equals the Chern number for the ground state of \stackrel\ifmmode \else \\fiH_f. In the limit m_f\ensuremath→0, the derivative of the Hall conductance with respect to m_f is proportional to ln|m_f|, with the constant of proportionality being the ratio of the change of W at m_f=0 to the energy gap in the initial state. This nonanalytic behavior is universal in two-band Chern insulators such as the Dirac model, the Haldane model, or the Kitaev honeycomb model in the fermionic basis.

Citations

• Dynamical quantum phase transitions in the Kitaev honeycomb model
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Topological insulators and superconductors
• Photovoltaic Hall effect in graphene
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Quench dynamics of edge states in 2-D topological insulator ribbons
• Quantum quench in ap+ipsuperfluid: Winding numbers and topological states far from equilibrium
• Anyons in an exactly solved model and beyond