adv

A many-body index for quantum charge transport. (arXiv:1810.07351v1 [math-ph])

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

Solidot 文章翻译

你的名字

留空匿名提交
你的Email或网站

用户可以联系你
标题

简单描述
内容