Valence bonds and the Lieb-Schultz-Mattis theorem
- 1 November 1989
- journal article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 40 (13), 8954-8960
- https://doi.org/10.1103/physrevb.40.8954
Abstract
The decoupling of short-range valence-bond states into topologically distinct sectors is discussed. On a square-lattice strip with odd width, this decoupling implies that short-range resonating-valence-bond (RVB) states are doubly degenerate. This result is precisely equivalent to the Lieb-Schultz-Mattis (LSM) theorem. Consequently short-range RVB states are consistent with the LSM theorem whether or not they possess gapless excitations. In the limit of infinite strip width, the decoupling becomes fourfold, in agreement with a recent conjecture of Haldane.Keywords
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