QUANTIZED DENSITY RESPONSE IN INSULATORS

The response of particle density to a dilation of a periodic potential in an insulator, with or without a fixed background potential or a ma gnetic field, is shown to be quantized. A similar phenomenon occurs in a quantum Hall system, where the derivative of the electron density w ith respect to the magnetic field is quantized in units of e/h, the in verse flux quantum. A number of other interesting results may be unifi ed under the notion of quantized density response, including the quant ization of adiabatic particle transport, the gap labeling theorem, and its generalization in the presence of a magnetic field.