Antiferromagnetic Heisenberg ladders in a staggered magnetic field
  We study the low-energy excitations of the spin-1/2 antiferromagnetic Heisenberg chain and $N$-leg ($N$=2, 3, 4) ladders in a staggered magnetic field $h_s$. We show that $h_s$ induces gap and midgap states in all the cases and examine their field scaling behavior. A modified boundary scheme is devised to extract accurate bulk excitation behavior. The gap values converge rapidly as $N$ increases, leading to a field scaling exponent $\gamma=1/2$ for both the longitudinal and transverse gaps of the square lattice ($N \to \infty$). The midgap states induced by the boundary edge effects share the bulk gap scaling exponents but their overall scaling behavior in the large-N limit needs further investigation. 
Jize Zhao, Xiaoqun Wang, Tao Xiang, Zhaobin Su, Lu Yu, Jizhong Lou and   Changfeng Chen