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arXiv:1012.5478 · Journal of Physics A Mathematical and Theoretical

Magnetic properties and thermal entanglement on a triangulated Kagomé lattice

N.S. Ananikian, L. Ananikyan, Levon Chakhmakhchyan, ARMEN N. KOCHARIAN

Published Dec 8, 2010• 23 citations
arXivHTMLPDF

Abstract

The magnetic and entanglement thermal (equilibrium) properties in spin-1/2 Ising-Heisenberg model on a triangulated Kagome lattice are analyzed by means of variational mean-field like treatment based on Gibbs-Bogoliubov inequality. Because of the separable character of Ising-type exchange interactions between the Heisenberg trimers the calculation of quantum entanglement in a self-consistent field can be performed for each of the trimers individually. The concurrence in terms of three qubit isotropic Heisenberg model in effective Ising field is non-zero even in the absence of a magnetic field. The magnetic and entanglement properties exhibit common (plateau and peak) features observable via (antferromagnetic) coupling constant and external magnetic field. The critical temperature for the phase transition and threshold temperature for concurrence coincide in the case of antiferromagnetic coupling between qubits. The existence of entangled and disentangled phases in saturated and frustrated phases is established.

DOI
10.1088/1751-8113/44/2/025001

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The magnetic and entanglement thermal (equilibrium) properties in spin-1/2 Ising-Heisenberg model on a triangulated Kagome lattice are analyzed by means of variational mean-field like treatment based on Gibbs-Bogoliubov inequality. Because of the separable character of Ising-type exchange interactions between the Heisenberg trimers the calculation of quantum entanglement in a self-consistent field can be performed for each of the trimers individually. The concurrence in terms of three qubit isotropic Heisenberg model in effective Ising field is non-zero even in the absence of a magnetic field. The magnetic and entanglement properties exhibit common (plateau and peak) features observable via (antferromagnetic) coupling constant and external magnetic field. The critical temperature for the phase transition and threshold temperature for concurrence coincide in the case of antiferromagnetic coupling between qubits. The existence of entangled and disentangled phases in saturated and frustrated phases is established.
The equilibrium magnetic and entanglement properties in a spin-1/2 Ising-Heisenberg model on a triangulated Kagomé lattice are analyzed by means of the effective field for the Gibbs-Bogoliubov inequality. The calculation is reduced to decoupled individual (clusters) trimers due to the separable character of the Ising-type exchange interactions between the Heisenberg trimers. The concurrence in terms of the three qubit isotropic Heisenberg model in the effective Ising field in the absence of a magnetic field is non-zero. The magnetic and entanglement properties exhibit common (plateau, peak) features driven by a magnetic field and (antiferromagnetic) exchange interaction. The (quantum) entangled and non-entangled phases can be exploited as a useful tool for signalling the quantum phase transitions and crossovers at finite temperatures. The critical temperature of order-disorder coincides with the threshold temperature of thermal entanglement.
The spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is exactly solved in a magnetic field within the framework of the generalized star-triangle transformation and the method of exact recursion relations. The generalized star-triangle transformation establishes an exact mapping correspondence with the effective spin-1/2 Ising model on a triangular Husimi lattice with a temperature-dependent field, pair and triplet interactions, which is subsequently rigorously treated by making use of exact recursion relations. The ground-state phase diagram of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice, which bears a close resemblance with a triangulated kagomé lattice, involves, in total, two classical and three quantum ground states manifested in respective low-temperature magnetization curves as intermediate plateaus at 1/9, 1/3, and 5/9 of the saturation magnetization. It is verified that the fractional magnetization plateaus of quantum nature have character of either dimerized or trimerized ground states. A low-temperature magnetization curve of the spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice resembling a triangulated kagome lattice may exhibit either no intermediate plateau, a single 1/3 plateau, a single 5/9 plateau, or a sequence of 1/9, 1/3, and 5/9 plateaus depending on a character and relative size of two considered coupling constants.
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 entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.
Magnetic properties and quantum entanglement of Heisenberg model with two-, three- and four-site exchange interactions on zigzag ladder are studied. Magnetic properties and concurrence (measure of quantum entanglement) are analyzed by means of variational mean-field-like treatment based on the Gibbs-Bogoliubov inequality. The magnetization plateau and second-order phase transition are obtained. A comparison of the entanglement and magnetic characteristics for the zigzag ladder is made. Our calculations show that in the antiferromagnetic region the behavior of the concurrence coincides with that of the magnetization.
Using Heisenberg model with two-, three- and four-site exchange interactions, by means of variational mean-feld like treatment based on Gibbs-Bogoliubov inequality the magnetic properties and concurrence (measure of pairwise thermal entanglement) on decorated zigzag ladder are studied. We have found that in the antiferromagnetic region behaviour of the concurrence coincides with the magnetic susceptibility one. With absence of external magnetic feld the dependence of magnetization from temperature plotted and shown that system undergo second order phase transition in some critical temperature.