Analytical and numerical studies of the one-dimensional sawtooth chain

By using the analytical coupled cluster method, the numerical exact diagonalization method, and the numerical density matrix renormalization group method, we investigated the properties of the one-dimensional sawtooth chain. The results of the coupled cluster method based on Neel state demonstrate that the ground state is in the quasi-Neel-long-range order state when α αc2α>αc2. The results of the coupled cluster method and the density matrix renormalization group method both disclose that the type of the quantum phase transition occurring at αc2αc2 belongs to the first-order transition.