Exact Ground State of One- and Two-Dimensional Frustrated Quantum Spin Systems

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

Joint Institute of Chemical Physics of RAS, 117977 Moscow, Russia Max-Planck-Institut fur Physik Komplexer Systeme, 01187 Dresden, Germany 

In this paper we present a set of ID and 2D spin-1/2 models with competing F and AF interactions for which the singlet ground-state wave function can be found exactly. This function has a special form expressed in terms of auxiliary Bose operators. This form of the wave function is similar to the MP one but with infinite matrices. For special values of model parameters it can be reduced to the standard MP form. 

It will be shown that proposed form of the exact wave function can be generalized to higher dimensions and a two dimensional frustrated spin model with exact ground state can be constructed. 

The paper is organized as follows. In See.2 we consider the frustrated spin chain at F-AF transition point and describe the exact singlet ground-state wave function as well as details of the spin correlation function calculations. We discuss the phase diagram of this model and its magnetic properties in the AF phase. In Sec.3 the special spin ladder will be considered. A two-dimensional frustrated spin model with the exact ground state is considered in Sec.4. Sec. 5 is devoted to the construction of the electronic models with the SB type of wave function. The results of this paper are summarized in Sec.6. 

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