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

The ground-state properties of the one-dimensional isotropic spin-1/2 Heisenberg antiferromagnet with antiferromagnetic first- and second-neighbor exchange interactions are discussed. The ground-state energy, the singlet-triplet energy gap, the Néel correlation function, the dimer correlation function, and the magnetization are calculated 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 depending on whether 0≤j≤j_c or j>j_c, where j is the ratio of the second- to the first-neighbor interaction constant and j_c=0.30 ±0.01. Dimer long-range order does exist in the finite-gap phase and it does not in the gapless phase, while no Néel long-range order exists in both phases.