Exact ground state of several quasi-two- and three-dimensional frustrated Heisenberg models

Takashi Tonegawa, Makoto Kaburagi, Noriya Ichikawa +1 more

Lorien X. Hayden, T. A. Kaplan, S. D. Mahanti

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.

Tokuro Shimokawa, Hiroki Nakano

We study the ground-state properties of the S=1/2 Heisenberg models on the quasi-onedimensional kagome strip lattices by the exact diagonalization and density matrix renormalization group methods. The models with two different strip widths share the same lattice structure in their inner part with the spatially anisotropic two-dimensional kagome lattice. When there is no magnetic frustration, the well-known Lieb-Mattis ferrimagnetic state is realized in both models. When the strength of magnetic frustration is increased, on the other hand, the Lieb-Mattis-type ferrimagnetism is collapsed. We find that there exists a non-Lieb-Mattis ferrimagnetic state between the Lieb-Mattis ferrimagnetic state and the nonmagnetic ground state. The local magnetization clearly shows an incommensurate modulation with long-distance periodicity in the non-Lieb-Mattis ferrimagnetic state. The intermediate non-Lieb-Mattis ferrimagnetic state occurs irrespective of strip width, which suggests that the intermediate phase of the two-dimensional kagome lattice is also the non-Lieb-Mattis-type ferrimagnetism.

А. А. Овчинников, V. Ya. Krivnov, Д. В. Дмитриев

Kengo Tanaka