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Comparing numerically evaluated excitation gaps of dimerized spin-1/2 XXZchains with the gap formula for the low-energy effective sine-Gordon theory, wedetermine coefficients d_xy and d_z of bosonized dimerization operators inspin-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_zsin(sqrt{4pi}phi(x)) + .... We also calculate the coefficients of both spin anddimer operators for the spin-1/2 Heisenberg antiferromagnetic chain with anearest-neighbor coupling J and a next-nearest-neighbor coupling J2 = 0.2411J.As applications of these coefficients, we present ground-state phase diagramsof dimerized spin chains in a magnetic field and antiferromagnetic spin ladderswith a four-spin interaction. The optical conductivity and electricpolarization of one-dimensional Mott insulators with Peierls instability arealso evaluated quantitatively.

Coefficients of bosonized dimer operators in spin-1/2 XXZ chains and their applications