Exact solution for a quantum spin-12Ising-Heisenberg orthogonal-dimer chain with Heisenberg intradimer and Ising interdimer interactions

Abstract

The quantum spin-$\frac{1}{2}$ orthogonal-dimer chain with the Heisenberg intradimer and Ising interdimer interactions in a magnetic field is considered by a rigorous approach. The model conserves the $z$ component of total spin on vertical Heisenberg bonds, and this property is used to calculate exactly the partition function using the transfer-matrix method. We have found the ground-state phase diagram of the given model in a magnetic field as well as the macroscopic degeneracy along field-induced transitions accompanied with the magnetization jumps. The model exhibits two intermediate fractional plateaux at one quarter and one half of the saturation magnetization. We have examined the effect of the exchange anisotropy in the $XXZ$ Heisenberg intradimer interaction on the ground state. It is shown that the one-quarter and one-half plateaux may disappear from the magnetization curve for the ferromagnetic Heisenberg intradimer interaction. We have also studied rigorously the effect of frustrated interactions on the thermodynamic and magnetic properties of the model and show how the macroscopic degeneracy of the ground state is reflected in the low-temperature behavior of the magnetization, entropy, and specific heat. A possibility of observing enhanced magnetocaloric effect during the adiabatic demagnetization is discussed in detail.