  Comparing numerically evaluated excitation gaps of dimerized spin-1/2 XXZ
chains with the gap formula for the low-energy effective sine-Gordon theory, we
determine coefficients d_xy and d_z of bosonized dimerization operators in
spin-1/2 XXZ chains, which are defined as (-1)j(S^x_j S^x_j+1 +S^y_j S^y_j+1) =
d_xy sin(\sqrt{4pi}phi(x))+ ... and (-1)^j S^z_j S^z_j+1 = d_z
sin(sqrt{4pi}phi(x)) + .... We also calculate the coefficients of both spin and
dimer operators for the spin-1/2 Heisenberg antiferromagnetic chain with a
nearest-neighbor coupling J and a next-nearest-neighbor coupling J2 = 0.2411J.
As applications of these coefficients, we present ground-state phase diagrams
of dimerized spin chains in a magnetic field and antiferromagnetic spin ladders
with a four-spin interaction. The optical conductivity and electric
polarization of one-dimensional Mott insulators with Peierls instability are
also evaluated quantitatively.
