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Chinese Physics B

Thermal entanglement of the spin-1 Ising–Heisenberg diamond chain with biquadratic interaction

Yidan Zheng, Zhu Mao, Bin Zhou

Published Jun 1, 2017• 3 citations
Publisher

Abstract

We investigate the thermal entanglement of the spin-1 Ising–Heisenberg diamond chain, which can be regarded as a theoretical model for the homometallic molecular ferrimagnet [ Ni 3 ( C 4 H 2 O 4 ) 2 − ( μ 3 − OH ) 2 ( H 2 O ) 4 ] n ⋅ ( 2 H 2 O ) n . Two cases, i.e., the isotropic Heisenberg (Ising–XXX) coupling model and anisotropic Heisenberg (Ising–XXZ) coupling model, are discussed respectively. The negativity is chosen as the measurement of the thermal entanglement. By means of the transfer-matrix approach, we focus on the effects of biquadratic interaction parameters on the negativity of the infinite spin-1 Ising–Heisenberg diamond chain. In the Ising–XXX coupling model, it is shown that for the case with ferromagnetic coupling the thermal entanglement can be induced by the biquadratic interaction, but the external magnetic field will suppress the occurrence of the entanglement induced by the biquadratic interaction. In the Ising–XXZ coupling model, for the case with antiferromagnetic coupling, due to the biquadratic interaction the effect of the anisotropy parameter on the entanglement will be suppressed at near-zero temperature. Moreover, the biquadratic interaction makes the threshold temperature increase. The effects of the external magnetic field on the thermal entanglement are also discussed, and it is observed that the entanglement revival phenomena exist in both models considered.

DOI
10.1088/1674-1056/26/7/070302

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We investigate the thermal entanglement of the spin-1 Ising–Heisenberg diamond chain, which can be regarded as a theoretical model for the homometallic molecular ferrimagnet [ Ni 3 ( C 4 H 2 O 4 ) 2 − ( μ 3 − OH ) 2 ( H 2 O ) 4 ] n ⋅ ( 2 H 2 O ) n . Two cases, i.e., the isotropic Heisenberg (Ising–XXX) coupling model and anisotropic Heisenberg (Ising–XXZ) coupling model, are discussed respectively. The negativity is chosen as the measurement of the thermal entanglement. By means of the transfer-matrix approach, we focus on the effects of biquadratic interaction parameters on the negativity of the infinite spin-1 Ising–Heisenberg diamond chain. In the Ising–XXX coupling model, it is shown that for the case with ferromagnetic coupling the thermal entanglement can be induced by the biquadratic interaction, but the external magnetic field will suppress the occurrence of the entanglement induced by the biquadratic interaction. In the Ising–XXZ coupling model, for the case with antiferromagnetic coupling, due to the biquadratic interaction the effect of the anisotropy parameter on the entanglement will be suppressed at near-zero temperature. Moreover, the biquadratic interaction makes the threshold temperature increase. The effects of the external magnetic field on the thermal entanglement are also discussed, and it is observed that the entanglement revival phenomena exist in both models considered.
We investigate the thermal entanglement in a spin-1/2 Ising–Heisenberg diamond chain, in which the vertical Heisenberg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii–Moriya (DM) interaction contributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including D z and D x , on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interaction, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters ( D z and D x ) have remarkably different influences on the entanglement. Different from the case D z , there is the non-monotonic variation of the concurrence with temperature in the case D x , and additionally the DM interaction D x can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case D x is larger than that of the case D z .
Most quantum entanglement investigations are focused on two qubits or some finite (small) chain structure, since the infinite chain structure is a considerably cumbersome task. Therefore, the quantum entanglement properties involving an infinite chain structure is quite important, not only because the mathematical calculation is cumbersome but also because real materials are well represented by an infinite chain. Thus, in this paper we consider an entangled diamond chain with Ising and anisotropic Heisenberg (Ising-XXZ) coupling. Two interstitial particles are coupled through Heisenberg coupling or simply two-qubit Heisenberg, which could be responsible for the emergence of entanglement. These two-qubit Heisenberg operators are interacted with two nodal Ising spins. An infinite diamond chain is organized by interstitial-interstitial and nodal-interstitial (dimer-monomer) site couplings. We are able to get the thermal average of the two-qubit operator, called the reduced two-qubit density operator. Since these density operators are spatially separated, we could obtain the concurrence (entanglement) directly in the thermodynamic limit. The thermal entanglement (concurrence) is constructed for different values of the anisotropic Heisenberg parameter, magnetic field, and temperature. We also observed the threshold temperature via the parameter of anisotropy, Heisenberg and Ising interaction, external magnetic field, and temperature.
The negativity ( N ) as a measure of thermal entanglement (TE) is studied for a two-qutrit spin-1 anisotropic Heisenberg XXZ chain with Dzyaloshinskii—Moriya (DM) interaction in an inhomogeneous magnetic field in detail. The effects of the DM interaction parameter D z on the thermal variation of the N for given values of the external magnetic field B , a parameter b which controls the inhomogeneity of B and the bilinear interaction parameters J x = J y ≠ J z are obtained. It is found that N persists to higher values and to higher temperatures for the higher values of ± D z and for the higher positive values of J z , i.e. in the antiferromagnetic (AFM) case. When J z < 0, the ferromagnetic (FM) case, and D z is small, and if J z is strong enough to compete with D z , N decreases. In addition, N declines with the increasing values of B and b .
Quantum entanglement is one of the most fascinating types of correlation that can be shared only among quantum systems. The Heisenberg chain is one of the simplest quantum chains which exhibits a reach entanglement feature, due to the Heisenberg interaction is quantum coupling in the spin system. The two particles were coupled trough XYZ coupling or simply called as two-qubit XYZ spin, which are the responsible for the emergence of thermal entanglement. These two-qubit operators are bonded to two nodal Ising spins, and this process is repeated infinitely resulting in a diamond chain structure. We will discuss two-qubit thermal entanglement effect on Ising-XYZ diamond chain structure. The concurrence could be obtained straightforwardly in terms of two-qubit density operator elements, using this result, we study the thermal entanglement, as well as the threshold temperature where entangled state vanishes. The present model displays a quite unusual concurrence behavior, such as, the boundary of two entangled regions becomes a disentangled region, this is intrinsically related to the XY-anisotropy in the Heisenberg coupling. Despite a similar property had been found for only two-qubit, here we show in the case of a diamond chain structure, which reasonably represents real materials.
In this paper, the entanglement in a spin-1 Heisenberg XXZ chain with uniform and nonuniform external magnetic field is investigated in the terms of the measure of entanglement called 'negativity'. The effects of the external magnetic field, the anisotropy parameter and the temperature on the negativity are discussed respectively. It can be seen that the entanglement in this spin chain for any temperature is symmetric with respect to zero magnetic field. We calculate the partially transposed density matrix and give qualitatively results at different temperatures. In order to show the results clearly, the behavior of negativity is presented for five different cases. It can be found that the temperature and the external magnetic field can effect the feature of the thermal entanglement significantly. In addition, under certain condition, the negativity may be enhanced under a nonuniform magnetic field.
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.