Tensor Network States for Chiral Topological Phases
summary
Claims that strictly short-range tensor-network constructions for free-fermion chiral/topological bands produce parent Hamiltonians that must be gapless when the occupied bundle is topologically nontrivial. Uses band theory, Gaussian Grassmann integrals and Fourier-space ratio of trigonometric polynomials to build states, then constructs compact-support annihilation operators by inverse Fourier transform. Explicit d=2, n=2 example has g(k) ~ 1/(kx + i ky), giving Chern number 1, a touching of filled and empty single-particle bands, and power-law correlations rather than a gapped ground state.
AI-written summary · about