Exact ground state of one- and two-dimensional frustrated quantum spin systems

Details Exact ground state of one- and two-dimensional frustrated quantum spin systems Exact ground state of one- and two-dimensional frustrated quantum spin systems

2001-05-15

arxiv.org/abs/cond-mat/0105295v1

Elsevier, Theor. and comp. Chem. Book Series, "Valence Bond Theory", 769-810 (2002)

Physics

Condensed Matter

Strongly Correlated Electrons

26 pages, 14 figures

Scientific paper

We outline the recent results on the ground state for a class of one- and two-dimensional frustrated quantum spin models with competing ferro(F)- and antiferromagnetic (AF) interactions. Frustrated spin systems are known to have many interesting properties due to large quantum fluctuations. As a result of these fluctuations usual mean-field approach gives quite crude (if not false) description of these systems. Therefore, exactly solvable models are very instructive at investigations of such systems. The exact ground state wave function of proposed models has a structure of the valence-bond state (VBS) type. One of the 1D model describes the transition line between the F and AF phase. The exact singlet ground state on this line has a double-spiral ordering. Using different approximation methods we study the magnetization curve in the AF phase. The second considered set of the 1D and 2D models has an exact non-degenerate ground state with exponentially decaying spin correlations. We also proposed the 1D and 2D electronic models with exact ground state represented in terms of singlet bond functions which are the generalization of the RVB functions including ionic states.

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