Ground-state long-range order in quasi-one-dimensional Heisenberg quantum antiferromagnets: High-order coupled-cluster calculations

We investigate the ground-state magnetic long-range order of quasi-one-dimensional quantum Heisenberg antiferromagnets for spin quantum numbers s=1/2 and s=1. We use the coupled cluster method to calculate the sublattice magnetization in dependence on the inter-chain coupling. We find that for the unfrustrated spin-1/2 system an infinitesimal inter-chain coupling is sufficient to stabilize magnetic long-range order, which is in agreement with results obtained by some other methods. For s=1 we find that a finite inter-chain coupling of about 10% of the in-chain coupling is necessary to stabilize magnetic long-range order. Furthermore, we consider a quasi one-dimensional spin-1/2 system, where a frustrating next-nearest neighbor in-chain coupling is included. We find that for stronger frustration also a finite inter-chain coupling is necessary to have magnetic long-range order in the ground state, where the strength of the inter-chain coupling necessary to establish magnetic long-range order is related to the size of the spin gap of the isolated chain.