Some remarks on the Lieb-Schultz-Mattis theorem and its extension to higher dimensions

Details Some remarks on the Lieb-Schultz-Mattis theorem and its extension to higher dimensions Some remarks on the Lieb-Schultz-Mattis theorem and its extension to higher dimensions

2000-02-11

arxiv.org/abs/cond-mat/0002170v1

Obsolete version. See Eur. Phys. J. B 26, 167 (2002) - cond-mat/0112360

Physics

Condensed Matter

Strongly Correlated Electrons

12 pages, LaTeX with 4 EPS figures embedded in the document

Scientific paper

10.1140/epjb/e20020078

The extension of the Lieb-Schultz-Mattis theorem to dimensions larger than one is discussed. It is explained why the variational wave-function built by the previous authors is of no help to prove the theorem in dimension larger than one. The short range R.V.B. picture of Sutherland, Rokhsar and Kivelson, Read and Chakraborty gives a strong support to the assertion that the theorem is indeed valid in any dimension. Some illustrations of the general ideas are displayed on exact spectra.

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