1207.7341 (Zhong Wang et al.)

Topological Hamiltonian as an Exact Tool for Topological Invariants    [PDF]

Zhong Wang, Binghai Yan

We propose the concept "topological Hamiltonian" for various topological insulators in interacting systems. Although a bad tool for calculating energy spectra, "topological Hamiltonian" is an exact tool in producing topological invariants. We also show that, unlike the topological Hamiltonian, the natural "effective Hamiltonian" for quasiparticles can produce wrong topological invariants, despite its ability to give us excellent energy spectra. We present a physical explanation for this counterintuitive phenomenon from the surface state picture, more precisely, we show that the topological Hamiltonian determines the existence or absence of gapless surface modes. This confirms the topological Hamiltonian instead of the mean field effective Hamiltonian as an exact tool for calculating topological invariants in interacting systems. This result has significant implications for analytical and numerical calculations of topological invariants in interacting systems, in particular, it shows that the conventional band structure calculations of topological invariant can fail.

View original: http://arxiv.org/abs/1207.7341