Many-body generalization of the Z2 topological invariant for the quantum spin Hall effect

Abstract

We propose a many-body generalization of the Z2 topological invariant for the quantum spin Hall insulator, which does not rely on single-particle band structures. The invariant is derived as a topological obstruction that distinguishes topologically distinct many-body ground states on a torus. It is also expressed as a Wilson-loop of the SU(2) Berry gauge field, which is quantized due to the time-reversal symmetry.

4 pages, 3 figures (final version to appear in Phys. Rev. Lett.)

References in corpus (4)

• Topological Insulators with Inversion Symmetry
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Topological aspects of quantum spin Hall effect in graphene: Z${}_2$ topological order and spin Chern number

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• Mott Physics on Helical Edges of 2D Topological Insulators
• A Fractionalized Quantum Spin Hall Effect
• Construction and properties of a topological index for periodically driven time-reversal invariant 2D crystals
• Topological Insulators and Superconductors from String Theory
• Topological meaning of Z${}_2$ numbers in time reversal invariant systems
• Entanglement Chern number for an extensive partition of a topological ground state
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Quantum distance and the Euler number index of the Bloch band in a 1D spin model
• The topological invariants of rotationally symmetric crystals
• Computing the ${\mathbb{Z}}_2$ Invariant in Two-Dimensional Strongly-Correlated Systems