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Journal Article

Lattice twist operators and vertex operators in sine-Gordon theory in one dimension


Nakamura,  M.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Nakamura, M., & Voit, J. (2002). Lattice twist operators and vertex operators in sine-Gordon theory in one dimension. Physical Review B, 65(15): 153110. Retrieved from http://ojps.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRBMDO000065000015153110000001&idtype=cvips&gifs=yes.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002B-37AC-F
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.