Cui-Hong Yang

Analytical and numerical studies of the one-dimensional sawtooth chain

Abstract 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 α c 1 . The translational symmetry of the ground state varies and the ground state evolves from the quasi-Neel-long-range order state to the dimerized state at the critical point α c 1 . The dimerized state is stable in the intermediate parameter region and vanishes at another critical point α c 2 . The results drawn from the exact diagonalization show that the precise critical points α c 1 and α c 2 can be determined by using the spin stiffness fidelity susceptibility and spin gap separately. We compared the results obtained by using the coupled cluster method based on canted state with those obtained based on spiral state, and found that the ground state of the sawtooth chain is in the quasi-canted state if α > α c 2 . 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 α c 2 belongs to the first-order transition.

Frustration Induced Noncollinear Magnetic Order Phase in One-Dimensional Heisenberg Chain with Alternating Antiferromagnetic and Ferromagnetic Next Nearest Neighbor Interactions

By using the coupled cluster method (CCM), the numerical exact diagonalization (ED) method, and the numerical density matrix renormalization group (DMRG) method, we investigated the properties of the one-dimensional Heisenberg chain with alternating antiferromagnetic and ferromagnetic next nearest neighbor interactions. In the classical limit, the ground state is in the collinear Neel state if α 1/2 there is an noncollinear canted state. For the quantum case, we found that, although the classical Neel state is absent, the canted state exists if the frustration parameter α exceeds a critical point αc1. Although there is another critical point αc2 in a finite system at which the ground state evolves from the canted state to the collinear Neel plus ferromagnetic state, that state is absent because αc2 tends to infinity in the thermodynamic limit. Thus, the quantum ground state phase diagram of the chain is composed of the collinear quasi-Neel state and canted state. The precise critical ...

Coupled Cluster Treatment of the Alternating Bond Diamond Chain

By the analytical coupled cluster method (CCM), we study both the ground state and lowest-lying excited-state properties of the alternating bond diamond chain. The numerical exact diagonalization (ED) method is also applied to the chain to verify the accuracy of CCM results. The ED results show that the ground-state phase diagram contains two exact spin cluster solid ground states, namely, the tetramer-dimer (TD) state and dimer state, and the ferrimagnetic long-range-ordered state. We prove that the two exact spin cluster solid ground states can both be formed by CCM. Moreover, the exact spin gap in the TD state can be obtained by CCM. In the ferrimagnetic region, we find that the CCM results for some physical quantities, such as the ground-state energy, the sublattice magnetizations, and the antiferromagnetic gap, are comparable to the results obtained by numerical methods. The critical line dividing the TD state from the ferrimagnetic state is also given by CCM and is in perfect agreement with that det...