Abstract
Using the bosonization technique and self-consistent quantum theory, we study two branches of low-lying excitation in the spin-Peierls system ${\mathrm{CuGeO}}_{3}$ with frustration. The energy gaps of triplet one-magnon excited state and singlet two-magnon bound state are calculated for a set of parameters appropriate to the compound ${\mathrm{CuGeO}}_{3}.$ The calculated results are consistent with experimental data of ${\mathrm{CuGeO}}_{3}.$ It is found that the energy gaps of the one- and two-magnon states increase with increasing either frustration or dimerization parameter. As the dimerization is increased, the binding energy of the singlet two-magnon bound state increases for smaller frustration, whereas it decreases for larger frustration. The power-law relation between the binding energy and the dimerization exists for small dimerization and at criticality $\ensuremath{\alpha}={\ensuremath{\alpha}}_{c}=0.2411.$
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