Dimer correlation amplitudes and dimer excitation gap in spin-1/2 XXZ and Heisenberg chains

Correlation functions of dimer operators, the product operators of spins on two adjacent sites, are studied in the spin-$\frac{1}{2}$ XXZ chain in the critical regime. The amplitudes of the leading oscillating terms in the dimer correlation functions are determined with high accuracy as functions of the exchange anisotropy parameter and the external magnetic field, through the combined use of bosonization and density-matrix renormalization group methods. In particular, for the antiferromagnetic Heisenberg model with SU(2) symmetry, logarithmic corrections to the dimer correlations due to the marginally-irrelevant operator are studied, and the asymptotic form of the dimer correlation function is obtained. The asymptotic form of the spin-Peierls excitation gap including logarithmic corrections is also derived.