Cluster-effective-field study on ground-state properties of quantum spin systems

Ola Bratteli, Akitaka Kishimoto, Derek W. Robinson

Johannes Richter

Ground-state properties of spin 1 / 2 Heisenberg systems are calculated for finite clusters up to nine spins. By a comparison of systems with different degrees of competition in the interactions, the frustration effects in the spin configuration of the ground state are investigated. A minimum value for the strength of the spin correlation mod <S i .S j > 0 mod of antiferromagnetically interacting spins i and j in systems without competition is estimated to be 0.25. The occurrence of values for mod <S i .S j < 0 mod lower than this minimum value indicates frustration. By varying the degree of competition, abrupt changes in the ground state are found. Furthermore the competition for certain systems causes ground states with much lower symmetry than that of the Hamiltonian.

Yoshihiko Nonomura, Masuo Suzuki

How to impose boundary conditions is crucial to finite-cluster calculations of quantum spin systems, but only open-boundary clusters have been used in cluster-effective-field approximations up to now. In the present paper, periodic-boundary clusters are also considered for the formulation of cluster-effective-field approximations in frustrated quantum spin systems. Namely, the open-boundary-condition double-cluster approximation (OBC-DCA) and the periodic-boundary-condition double-cluster approximation (PBC-DCA) are applied to the one-dimensional S= 1/2 frustrated XXZ model at the ground state. These two approximations are compared using the coherent-anomaly method (CAM). Within the limitation of cluster sizes in exact-diagonalization calculations, the PBC-DCA can reproduce the true phase boundary of the Neel-dimer transition. On the other hand, the OBC-DCA severely underestimates the existence of magnetic orders as quantum fluctuation is increased. These findings suggest that previous cluster-effective-field studies based on open-boundary clusters should be reconsidered.

Yoshihiko Nonomura

Antonis N. Andriotis, Eleftherios N. Economou, C. M. Soukoulis

The authors use an unrestricted self-consistent mean-field approach to the one-dimensional periodic Hubbard model to study its ground-state phase diagram. Their approach allows one to incorporate spin and electron correlations as well as spin and charge fluctuations. The authors find that a homogeneous antiferromagnetic state exists only at half-filling, where the state is also insulating. Off half-filling, it was found that the ground state of the Hubbard model consists of clusters with different magnetic and charge properties. For certain values of the parameters of the system the cluster formation develops to a full phase separation. The effects of the intersite repulsive or attractive interaction on the ground-state properties were also examined. Implications of the authors results for the existence of a superconducting ground state as well as comparison with other studies will be briefly discussed.

Laurens Vanderstraeten