We present a self-consistent quantum-theoretical analysis of the
ground-state energy and low-energy excitation spectrum of a dimerized and
frustrated Heisenberg chain by the bosonization representation in the
continuum-limit approach. The frustration effects on the ground-state energy
and energy gap are investigated for α>αc where α is
the frustration parameter and αc is its critical value, above
which a frustration-induced energy gap is opened. It is shown that as
α increases, the ground-state energy decreases and the energy gap
increases. We find that the dimerization dependence of the ground-state energy and energy
gap for small dimerization obeys the Cross-Fisher power law only
at α = αc, but departs significantly from it when
α>αc. The present results are in good agreement with
numerical analyses from the density-matrix renormalization-group and exact
diagonalization methods. The relevance of our calculated results to recent
experiments on the spin-Peierls compounds CuGeO3 is also discussed.
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