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Journal of Physics Conference Series

Magnetization Plateaus and Thermal Entanglement of Spin Systems

N.S. Ananikian, Č. Burdík, L. Ananikyan, Hasmik Poghosyan

Published Jan 1, 2017• 2 citations
Publisher

Abstract

The geometrically magnetic frustrations and quantum thermal entanglement of antiferromagnetic metal-containing compounds are considered on a diamond chain. We researched the magnetic and thermal properties of the symmetric Hubbard dimers with delocalized interstitial spins and the quantum entanglement states. It is presented magnetization plateaus and negativity in spin-1 Ising-Heisenberg model using transfer matrix technique. Applying the dynamic system approach we study the magnetic curves, Lyapunov exponents and superstable point in the two-dimensional mapping for the partition function of spin-1 classical and Ising-Heisenberg models at T → 0 on a diamond chain.

DOI
10.1088/1742-6596/804/1/012002

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The exact solution of the distorted Ising-Hubbard model for a diamond chain is obtained by means of transfer matrix method. Based on this solution the magnetic, thermal and concurrence properties of the system are studied. We discuss in detail the ground state varying values of Ising and Hubbard interaction couplings, hopping amplitude, magnetic field, chemical potential and get paramagnetic, ferromagnetic, antiferromagnetic and ferrimagnetic phases of the system. Plateaus in magnetization curves and several-peak structures of the specific heat curve for different values of Hamiltonian parameters are obtained. The dependence of concurrence in Hubbard dimers from chain parameters, external magnetic field and temperature are studied.
Abstract We study spin-1 antiferromagnetic Ising–Heisenberg models on diamond chains with biquadratic nodal–nodal interactions, focusing on the emergence of superstable points and cycles. Using recurrence relations to derive multidimensional rational mappings, we analyze their stability via the maximum Lyapunov exponent. This reveals a clear link between dynamical features and magnetization plateaus. Our results highlight how super-stable behavior reflects key aspects of the system’s magnetic and dynamic properties across various parameter regimes.
Abstract This study is devoted to the discovery of super-stable points and cycles in antiferromagnetic Ising and Ising-Heisenberg models with spin 1 on diamond chains with nodal-nodal interactions. These phenomena are important for understanding the complex behavior of magnetic systems. We specifically investigate their connection with magnetization plateaus, which serve as critical indicators of the model’s characteristics. Employing the recurrence relations technique, we derive multidimensional rational mappings that give insights about the statistical properties of the models. Carefully examining the stability properties of these mappings, in particular, by analyzing the maximum Lyapunov exponent, we have revealed the complex relationship between the magnetization plateau and dynamic properties. Throughout our extensive research, we have comprehensively studied the existence and behavior of super-stable points and cycles for various parameter configurations in spin-1 models on the diamond chains. By highlighting the basic properties of dynamics and stability, our research advances a fundamental understanding of complex magnetic systems and their fascinating properties.
The entanglement thermal (equilibrium) properties in spin-1/2 Ising-Heisenberg model on an ideal diamond chain is analyzed. Due to the classical character of Ising-type exchange interactions between two neighboring antiferromagnetic Heisenberg dimers, the calculation of quantum entanglement (by tracing out Ising spins) can be performed for each of the dimers separately. The concurrence, as a measure of entanglement is obtained and different regimes depending on the values of exchange interactions are revealed. The effects of the magnetic field are incorporated and critical temperatures corresponding to the vanishing or arising of entanglement are considered.
The exactly solvable spin-1/2 Ising-Heisenberg distorted diamond chain in the presence of the external magnetic field is investigated for the case of antiferromagnetic Ising and ferromagnetic XXZ Heisenberg interactions. The influence of quantum fluctuations and the distortion on the ground state, magnetic and thermal properties of the model are studied in detail.In particular, it is established that the zero-temperature magnetization curve may involve intermediate plateaus just at zero and 1/3 of the saturation magnetization. It is demonstrated that the temperature dependence of the specific heat reveals up to four distinct peaks at zero magnetic field and up to five distinct peaks at a weak magnetic field. The physical origin of all observed additional peaks of the specific heat has been clarified on the grounds of dominating thermal excitations. We have shown that the quantum fluctuations give rise to an effective geometrical frustration in this chain.