The properties of the spin-1/2 double chain Heisenberg antiferromagnet are studied by means of the numerical diagonalization and the projector Monte Carlo simulation. The model consists of the two spin 1/2 antiferromagnetic quantum Heisenberg chains coupled with each other via the ferromagnetic interchain coupling J ′ . It is shown that the first excited state has a gap for large enough J ′ . This gap continues to the Haldane gap in the limit J ′ →∞, where spins on the different chains form triplets on each site. On the other hand, the gap decreases rapidly between J ′ =1.0 and 0.6 and is undetectable for J ′ <0.6 within the present accuracy.
The double chain Heisenberg antiferromagnet with anisotropy is studied using the mapping onto the coupled anisotropic nonlinear σ model. This model consists of two anisotropic antiferromagnetic quantum Heisenberg chains with half-integer spin coupled with each other via the ferromagnetic interchain coupling J '. For small J ', our analysis suggests that J ' is an irrelevant parameter and consequently the two chains behave independently and no gap is generated. On the other hand, for large enough J ', the two chains behave as a single Heisenberg chain with integer spin which has a gap in the excitation spectrum. The expected behavior in the isotropic limit is also discussed.