Heisenberg - Ising magnets

Ôjirô Nagai, Yuuzi Yamada, Y. Miyatake

Hamid Arian Zad, Vadim Ohanyan, Azam Zoshki +1 more

The ground state, entropy, and magnetic Grüneisen parameter of the antiferromagnetic spin-1/2 Ising-Heisenberg model on a double sawtooth ladder are rigorously investigated using the classical transfer-matrix technique. The model includes the XXZ interaction between the interstitial Heisenberg dimers, the Ising coupling between nearest-neighbor spins of the legs and rungs, and additional cyclic four-spin Ising term in each square plaquette. For a particular value of the cyclic four-spin exchange, we found in the ground-state phase diagram of the Ising-Heisenberg ladder a quadruple point, at which four different ground states coexist together. During an adiabatic demagnetization process, a fast cooling accompanied with an enhanced magnetocaloric effect can be detected near this quadruple point. The ground-state phase diagram of the Ising-Heisenberg ladder is confronted with the zero-temperature magnetization process of the purely quantum Heisenberg ladder, which is calculated by using exact diagonalization based on the Lanczos algorithm for a finite-size ladder of 24 spins and the density-matrix renormalization group simulations for a finite-size ladder with up to 96 spins. Some indications of the existence of intermediate magnetization plateaus in the magnetization process of the full Heisenberg model for a small but nonzero four-spin Ising coupling were found. The DMRG results reveal that the quantum Heisenberg double sawtooth ladder exhibits some quantum Luttinger spin-liquid phase regions that are absent in the Ising-Heisenberg counterpart model. Except this difference, the magnetic behavior of the full Heisenberg model is quite analogous to its simplified Ising-Heisenberg counterpart and, hence, may bring insight into the fully quantum Heisenberg model from rigorous results for the Ising-Heisenberg model.

V. E. Korepin, N. M. Bogoliubov, Anatoli G. Izergin

Bohdan Lisnyi

The ground state of the spin-1/2 Ising–Heisenberg distorted diamond chain in the presence of an external magnetic field is investigated in the case of the ferromagnetic Ising and antiferromagnetic XXZ Heisenberg interactions, that exhibits a geometric frustration of spins. The influence of the quantum fluctuations, the magnetic field, and the distortion on the ground state are studied in detail. It is established that the zero-temperature magnetization curve may show intermediate plateaus at zero and one-third of the saturation magnetization.

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