Note on Green Function Formalism and Topological Invariants

Abstract

It has been discovered previously that the topological order parameter could be identified from the topological data of the Green's function, namely the (generalized) TKNN invariant in general dimensions, for both non-interacting and interacting systems. In this note, we show that this phenomenon has a clear geometric derivation. This proposal could be regarded as an alternative proof for the identification of the corresponding topological invariant and the topological order parameter.

19 pages, 3 figures

References in corpus (4)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Interacting topological phases and modular invariance
• Topological field theory and thermal responses of interacting topological superconductors
• Topological invariants for interacting topological insulators with inversion symmetry

Cited by in corpus (2)

• Optical $N$-invariant of graphene's viscous Hall fluid
• Optical $N$-insulators: topological obstructions in the atomistic susceptibility tensor