  We study the nature of edge states in extrinsically and spontaneously
dimerized states of two-dimensional spin-1/2 antiferromagnets, by performing
quantum Monte Carlo simulation. We show that a gapless edge mode emerges in the
wide region of the dimerized phases, and the critical exponent of spin
correlators along the edge deviates from the value of Tomonaga-Luttinger (TL)
liquid universality in large but finite systems at low temperatures. We also
demonstrate that the gapless nature at edges is stable against several
perturbations such as external magnetic field, easy-plane XXZ anisotropy,
Dzyaloshinskii-Moriya interaction, and further-neighbor exchange interactions.
The edge states exhibit non TL-liquid behavior, depending strongly on model
parameters and kinds of perturbations. Possible ways of detecting these edge
states are discussed. Properties of edge states we show in this paper could
also be used as reference points to study other edge states of more exotic
gapped magnetic phases such as spin liquids.
