Electric polarization as a nonquantized topological response and boundary Luttinger theorem
Abstract
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 $2\pi$flux. In $3d$ the polarization is determined by the projective representation of translation symmetries on Dirac monopoles. Our approach also leads to a concrete scheme to calculate polarization in $2d$, which in principle can be applied even to strongly interacting systems. For open boundary condition, the bulk polarization leads to an altered `boundary' Luttinger theorem (constraining the Fermi surface of surface states) and also to modified LiebSchultzMattis theorems on the boundary, which we derive.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.08637
 Bibcode:
 2019arXiv190908637S
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 7+8 pages, 3 figures, updated discussion on magnetic translations