Chapter 23 Exact ground states of one- and two-dimensional frustrated quantum spin systems

Abstract

Summary We outline the recent results for the ground states 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 the usual mean-field approach gives a quite crude (if not false) description of these systems. Therefore, exactly solvable models are very instructive for investigations of such systems. The exact ground state wave function of the proposed models has a structure of the valence-bond state (VBS) type. One of the ID 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 ID and 2D models has an exact non-degenerate ground state with exponentially decaying spin correlations. We also propose the ID and 2D electronic models with exact ground states represented in terms of singlet bond functions which are a generalization of the RVB functions including ionic states.