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Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension

Masaaki Nakamura·Johannes Voit
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Abstract

In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twisting operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values $z_L$ measure the overlap between the unique ground state and an excited state. Insulators are characterized by $z_{\infty}\neq 0$. 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 model. We apply this theory to the half-filled extended Hubbard model and obtain agreement with the level-crossing approach.

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Masaaki Nakamura, Johannes Voit. 2001-06-04. Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension. https://doi.org/10.1103/physrevb.65.153110

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