Elementary excitations in dimerized and frustrated Heisenberg chains

We present a detailed numerical analysis of the low-energy excitation spectrum of a frustrated and dimerized spin $S=1/2\mathrm{}$ Heisenberg chain. In particular, we show that in the commensurate spin-Peierls phase the ratio of the singlet and triplet excitation gap is a universal function which depends on the frustration parameter only. We identify the conditions for which a second elementary triplet branch in the excitation spectrum splits from the continuum. We compare our results with predictions from the continuum limit field theory. We discuss the relevance of our data in connection with recent experiments on ${\mathrm{CuGeO}}_3,$ ${\mathrm{NaV}}_2{\mathrm{O}}_5,$ and $(\mathrm{VO}{)}_2{\mathrm{P}}_2{\mathrm{O}}_7$.