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A many-body index for quantum charge transport. (arXiv:1810.07351v1 [math-ph])
来源于:arXiv
We propose an index for gapped quantum lattice systems that conserve a
$\mathrm{U}(1)$-charge. This index takes integer values and it is therefore
stable under perturbations. Our formulation is general, but we show that the
index reduces to (i) an index of projections in the non-interacting case, (ii)
the filling factor for translational invariant systems, (iii) the quantum Hall
conductance in the two-dimensional setting without any additional symmetry.
Example (ii) recovers the Lieb-Schultz-Mattis theorem, (iii) provides a new and
short proof of quantization of Hall conductance in interacting many-body
systems. Additionally, we provide a new proof of Bloch's theorem on the
vanishing of ground state currents. 查看全文>>