In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twist operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values z(L)((q)) measure the overlap between the q-fold degenerate ground state and an excited state. Insulators are characterized by z(infinity)not equal0, and different states are distinguished by the sign of z(L). We identify z(L) with ground-state expectation values of vertex operators in the sine-Gordon model. This allows an accurate detection of quantum phase transitions in the universality classes of the Gaussian and the SU(2)(1) Wess-Zumino-Novikov-Witten models. We apply this theory to the half-filled extended Hubbard model and obtain agreement with the level-crossing method.