Ground-State Properties of the One-Dimensional Isotropic Spin-1/2 Heisenberg Antiferromagnet with Competing Interactions

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The ground-state properties of the one-dimensional isotropic spin-1/2 Heisenbergantiferromagnet with antiferromagnetic first- and second-neighbor exchange interac-lions are discussed. The ground-state energy, the singlet-triplet energy gap, the Neelcorrelation function, the dimer correlation function, and the magnetization arecalculated exactly for finite-size systems up to 20 spins. By extrapolating these results,the values of the above quantities at the infinite-size limit are estimated. In particular,it is found that the limiting ground state is in the gapless or finite-gap phase depend-ing on whether Q,<ysy. or j>j., where j is the ratio of the second- to the first-neighbor interaction constant and j.= 0.30 8 0.01. Dimer long-range order does existin the finite-gap phase and it does not in the gapless phase, wltile no Neel long-rangeorder exists in both phases.
1987-06-15