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Journal of Physics Conference Series

Magnetization and concurrence on decorated zigzag ladder

N.S. Ananikian, Č. Burdík, H. A. Lazaryan

Published Feb 8, 2012• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1742-6596/343/1/012065

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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.
We consider a two-chain, spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg spin ladder in an external magnetic field HHH. The spin ladder is known to undergo second-order quantum phase transitions (QPTs) at two critical values Hc1{H}_{c1}Hc1​ and Hc2{H}_{c2}Hc2​ of the magnetic field. There are now known examples of strongly coupled (where the rung exchange interaction is much stronger than the nearest-neighbor intrachain exchange interaction) organic ladder compounds in which QPTs have been experimentally observed. In this paper, we investigate whether well-known bipartite entanglement meaures such as one-site von Neumann entropy, two-site von Neumann entropy, and concurrence develop special features close to the quantum critical points. As suggested by an earlier theorem, the first derivatives of the measures with respect to magnetic field are expected to diverge as $H\ensuremath{\rightarrow}{H}_{c1}$ and $H\ensuremath{\rightarrow}{H}_{c2}$. Based on numerical diagonalization data and a mapping of the strongly coupled ladder Hamiltonian onto the XXZXXZXXZ chain Hamiltonian, for which several analytical results are known, we find that the derivatives of the entanglement measures diverge as $H\ensuremath{\rightarrow}{H}_{c2}$ but remain finite as $H\ensuremath{\rightarrow}{H}_{c1}$. The reason for this discrepancy is analyzed. We further calculate two recently proposed quantum information theoretic measures, the reduced fidelity and reduced fidelity susceptibility, and show that these measures provide appropriate signatures of the QPTs occuring at the critical points H=Hc1H={H}_{c1}H=Hc1​ and H=Hc2H={H}_{c2}H=Hc2​.
We consider the Heisenberg model with two-, and three-spin exchange interactions on a zigzag ladder in a strong magnetic field. Using the recursion method for the partition function in Ising approximation we have found exact results for the magnetization. We have shown the existence of magnetization plateaus in the case of mutual two-, and three-spin exchanges at low temperatures and different exchange parameters. The system exhibits different magnetic behaviors, depending on the values of the exchange parameters.
We have established a quantum antiferromagnetic Heisenberg-Ising model on a spin-1/2 pyrochlore edge-shared ladder with Heisenberg intra-rung and Ising inter-rung interactions as a perspicuous candidate to exhibit magnetization mid and zero plateaus, characteristic peaks of magnetic susceptibility, and thermal entanglement mid plateau. The model is exactly solvable and thus, all the essential properties such as the thermal entanglement and the magnetic properties of the system can be exactly calculated. The calculations are done both through the transfer matrix technique and through the reduced density matrix. The magnetization plateaus are observed at zero and half the saturation value and the magnetic susceptibility exhibits a clear demonstration of the associated characteristic peaks. The model also displays the mid plateau of the thermal entanglement as a function of the external magnetic field at low temperatures.