Ground-state properties of linear-exchange quantum spin models

Abstract

We study a class of one-dimensional antiferromagnetic quantum spin-1/2 models using DMRG. The exchange interaction in these models decreases linearly with the separation between the spins, Jij = R − |i − j| for |i − j| < R, where R is a positive integer ⩾2. For |i − j| ⩾ R, the interaction is zero. It is known that all the odd-R models have the same exact dimer ground state as the Majumdar-Ghosh (MG) model. In fact, R = 3 is the MG model. However, for an even R, the exact ground state is not known in general, except for R = 2 (the integrable nearest-neighbor Heisenberg chain) and the asymptotic limit of R in which the MG dimer state emerges as the exact ground state. Therefore, we numerically study the ground-state properties of the finite even-R ≠ 2 models, particularly for R = 4, 6 and 8. We find that, unlike R = 2, the higher even-R models are spin-gapped, and exhibit robust dimer order of the MG type in the ground state. The spin-spin correlations decay rapidly to zero, albeit showing weak periodic revivals.