Excitation gap of an antiferromagnetic Heisenberg chain with multiple decorations

A one-dimensional spin- antiferromagnetic Heisenberg model with multiple decorations is introduced. The low-lying properties of the decorated quantum spin chain are discussed. In the continuum and semiclassical limit of the present model, the non-linear sigma model with a topological term is derived and the conjecture for the low-lying state is proposed. Validity of the conjecture seems to be supported by the perturbational expansions and by the density matrix renormalization group calculations.