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Using mainly numerical methods, we investigate the width of the spin gap of a spin‐1/2 two‐leg ladder described by  ${\cal H} = J_{{\rm l}} \sum\nolimits_{j = 1}^{N/2} {} [{\bf S}_{j,a} \cdot {\bf S}_{j + 1,a} + {\bf S}_{j,b} \cdot {\bf S}_{j + 1,b} ] + J_{{\rm r}} \sum\nolimits_{j = 1}^{N/2} {} [\lambda (S_{j,a}^{x} S_{j,b}^{x} + S_{j,a}^{y} S_{j,b}^{y} ) + S_{j,a}^{z} S_{j,b}^{z} ]$ , where  $S_{j,a(b)}^{\alpha } $  denotes the  α ‐component of the spin‐1/2 operator at the  j ‐th site of the  a  ( b ) chain. We mainly focus on the  $J_{{\rm r}}$  ≫  $J_{{\rm l}} > 0$  and  $|\lambda |\ll 1$  case. The width of the spin gap between the  M  = 0 and 1 subspaces ( M  is the total magnetization) as a function of  λ  anomalously increases near  λ  = 0; for instance, for  $- 0.1 $  ≲  $\lambda$  ≲  $0.1$  when  J  l / J  r  = 0.1. The gap formation mechanism is thought to be different for the  λ  < 0 and  λ  > 0 cases. Since, in usual cases, the width of the gap becomes zero or small at the point where the gap formation mechanism changes, the above gap‐increasing phenomenon in the present case is anomalous. We explain the origin of this anomalous phenomenon by use of the degenerate perturbation theory. We also draw the ground‐state phase diagram.

Anomalous behavior of the spin gap of a spin‐1/2 two‐leg antiferromagnetic ladder with Ising‐like rung interactions