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

2001/06/04 by Masaaki Nakamura, Johannes Voit · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Spectral Theory in Mathematical Physics #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.65.153110

4 pages, 3 figures

arxiv created 2001/06/04 · openalex publication_date 2002/04/12 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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_\ensuremath∞\ensuremath≠0, 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.

Citations

• Berry’s phase for energy bands in solids
• The critical properties of the two-dimensional xy model
• Two soluble models of an antiferromagnetic chain

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