Quantum topological excitations:: from the sawtooth lattice to the Heisenberg chain

From the recently determined structure of the delafossite YCuO2.5, we argue that the Cu-O network has nearly independent A chains but with different interactions between the s = 1/2 spins. Motivated by this observation, we study the A chain for different ratios of the base-base and base-vertex interactions, J(bb)/J(bv). By exact diagonalization and extrapolation, we show that the elementary excitation spectrum is the same for total spins S-tot = 0 and 1, but not for S-tot = 2, and has a gap only in the interval 0.4874(1) less than or equal to J(bb)/J(bv) less than or equal to 1.53(1). The gap, known to be dispersionless for J(bb)/J(bv), is found to acquire increasing k-dependence as J(bb)/J(bv) moves away from unity.