Electric polarization as a nonquantized topological response and boundary Luttinger theorem

@article{Song2019ElectricPA,
  title={Electric polarization as a nonquantized topological response and boundary Luttinger theorem},
  author={Xue Song and Yin-chen He and Ashvin Vishwanath and Chong Wang},
  journal={arXiv: Mesoscale and Nanoscale Physics},
  year={2019}
}
We develop a nonperturbative approach to the bulk polarization of crystalline electric insulators in $d\geq1$ dimensions. Formally, we define polarization via the response to background fluxes of both charge and lattice translation symmetries. In this approach, the bulk polarization is related to properties of magnetic monopoles under translation symmetries. Specifically, in $2d$ the monopole is a source of $2\pi$-flux, and the polarization is determined by the crystal momentum of the $2\pi… 

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