Analytical approach to dimerized and frustrated Heisenberg chains

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 alpha > alpha (c) where alpha is the frustration parameter and alpha (c) is its critical value, above which a frustration-induced energy gap is opened. It is shown that as a 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 alpha = alpha (c), but departs significantly from it when alpha > alpha (c). 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.