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Register a new userA Question: Quantum Critical Phenomena in XY Spin-Chain Systems With Dzyaloshinskii-Moriya Interactions
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Jordan-Wigner transformation and Bogolyubov transformation are the main steps of the diagonalization of Hamiltonian and paly an important role in the statistical mechanics calculations for one-dimensional Heisenberg spin chain model. Many methods can be exploited as a tool to detect quantum phase transition, regions of criticality and scaling behavior in the vicinity of a quantum phase transition, such as geometric phase, fidelity susceptibility, order parameter, and entanglement entropy, which have direct relation with Bogolyubov transformation. We diagonalized the Hamiltonian in XY spin-chain systems with Dzyaloshinskii-Moriya interactions, the results shows that only the energy spectrum but not the coefficients of the Bogolyubov transformation depends on DM interaction. Therefore, the DM interaction may not influence the critical magnetic field of quantum phase transitions and not induce new critical regions in the XY spin model. Moreover, we further prove the ideas by the methods of geometric phases in this model.
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The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii--Moriya (DM) interaction considered as Gaussian distribution, the entanglement in one-dimensional random $XY$ spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. (i) For ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglement below and above critical DM interaction. (ii) For antiferromagnetic spin chain, DM interaction can enhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity and exchange couplings (or magnetic field) play competing roles in enhancing quantum entanglement.
In order to explore the effect of external temperature $T$ in quantum correlation we compute thermal entanglement and thermal discord analytically in the Heisenberg $X$ $Y$ $Z$ model with Dzyaloshinskii-Moriya Interaction term ${bm D} cdot left( {bm sigma}_1 times {bm sigma}_2 right)$. For the case of thermal entanglement it is shown that quantum phase transition occurs at $T = T_c$ due to sudden death phenomenon. For antiferromagnetic case the critical temperature $T_c$ increases with increasing $|{bm D}|$. For ferromagnetic case, however, $T_c$ exhibits different behavior in the regions $|{bm D}| geq |{bm D_*}|$ and $|{bm D}| < |{bm D_*}|$, where ${bm D_*}$ is particular value of ${bm D}$. It is shown that $T_c$ becomes zero at $|{bm D}| = |{bm D_*}|$. We explore the behavior of thermal discord in detail at $T approx T_c$. For antiferromagnetic case the external temperature makes the thermal discord exhibit exponential damping behavior, but it never reaches to exact zero. For ferromagnetic case the thermal entanglement and thermal discord are shown to be zero simultaneously at $T_c = 0$ and $|{bm D}| = |{bm D_*}|$. This is unique condition for simultaneous disappearance of thermal entanglement and thermal discord in this model.
In this paper, we study the thermal entanglement in a two-qubit Heisenberg XYZ system with different Dzyaloshinskii-Moriya (DM) couplings. We show that different DM coupling parameters have different influences on the entanglement and the critical temperature. In addition, we find that when $J_{i}$ ($i$-component spin coupling interaction) is the largest spin coupling coefficient, $D_{i}$ ($i$-component DM interaction) is the most efficient DM control parameter, which can be obtained by adjusting the direction of DM interaction.
By using the method of density-matrix renormalization-group to solve the different spin-spin correlation functions, the nearest-neighbouring entanglement(NNE) and next-nearest-neighbouring entanglement(NNNE) of one-dimensional alternating Heisenberg XY spin chain is investigated in the presence of alternating nearest neighbour interactions of exchange couplings, external magnetic fields and next-nearest neighbouring interactions. For dimerized ferromagnetic spin chain, NNNE appears only above the critical dimerized interaction, meanwhile, the dimerized interaction effects quantum phase transition point and improves NNNE to a large value. We also study the effect of ferromagnetic or antiferromagnetic next-nearest neighboring (NNN) interactions on the dynamics of NNE and NNNE. The ferromagnetic NNN interaction increases and shrinks NNE below and above critical frustrated interaction respectively, while the antiferromagnetic NNN interaction always decreases NNE. The antiferromagnetic NNN interaction results to a larger value of NNNE in comparison to the case when the NNN interaction is ferromagnetic.
The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. [Phys. Rev. A 72, 012331 (2005)]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For generating W-state and GHZ-state a single qubit rotation is applied on second and all the three qubits respectively after the unitary evolution of the XY Hamiltonian.
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