The Heisenberg model

Jana Čisárová, Frédéric Michaud, Frédéric Mila +1 more

The ground state and zero-temperature magnetization process of the spin-1/2 Ising-Heisenberg model on two-dimensional triangles-in-triangles lattices are exactly calculated using eigenstates of the smallest commuting spin clusters. Our ground-state analysis of the investigated classical-quantum spin model reveals three unconventional dimerized or trimerized quantum ground states besides two classical ground states. It is demonstrated that the spin frustration is responsible for a variety of magnetization scenarios with up to three or four intermediate magnetization plateaus of either quantum or classical nature. The exact analytical results for the Ising-Heisenberg model are confronted with the corresponding results for the purely quantum Heisenberg model, which were obtained by numerical exact diagonalizations based on the Lanczos algorithm for finite-size spin clusters of 24 and 21 sites, respectively. It is shown that the zero-temperature magnetization process of both models is quite reminiscent, and hence, one may obtain some insight into the ground states of the quantum Heisenberg model from the rigorous results for the Ising-Heisenberg model even though exact ground states for the Ising-Heisenberg model do not represent true ground states for the pure quantum Heisenberg model.

J. Matysiak, R. Lemański

We perform exact numeric calculations for a few versions of the two-orbital Hubbard model on the four site cluster.We show that the conventional spin 1 Heisenberg Hamiltonian can be obtained in the strong coupling limit, but only for some versions of the two-orbital Hubbard model.Then we propose a modified version of the Heisenberg Hamiltonian, that we call the two-orbital Heisenberg model, which is relevant in those cases, where the conventional spin 1 Heisenberg model fails.

R. D. Poshusta, Thomas G. Schmalz, Douglas J. Klein

Pariser-Parr-Pople, Hubbard, and Heisenberg models for systems with one electron per site, such as the π-networks of neutral conjugated hydrocarbons, are considered. It is argued that for usual systems the Hubbard model describes reasonably only those states that are also capable of being so described by a Heisenberg model. Such Heisenberg models are given by a cluster expansion, surpassing in accuracy the results of correspondingly low-order degenerate perturbation expansions.

Lisa Paul Streitfeld