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Laser Physics Letters

Multipartite entanglement and quantum phase transitions in the XXZ model with Dzyaloshinskii–Moriya interaction

Tingting Wang, Jiadong Shi

Published Apr 30, 2019• 3 citations
Publisher

Abstract

Abstract With the aid of the quantum renormalization group (QRG) method, we study the multipartite entanglement and quantum phase transitions (QPTs) in the XXZ model with Dzyaloshinskii–Moriya (DM) interaction. The measures employed here are genuine multipartite entanglement (GME-concurrence) and global entanglement. The results show that both multipartite entanglement measures can accurately detect QPTs at the critical points after sufficient iteration steps. By the difference analysis, moreover, we derive an inequality such that the global entanglement is exactly an upper bound of the square GME-concurrence. Actually, this inequality is established whether or not the QRG method is carried out, which discloses some intrinsic features of long-scale multipartite entanglement. Based on the first derivative of GME-concurrence, the non-analytic phenomenon and scaling behaviors with different theoretical exponents are analyzed in detail, showing that the ground states of the XXZ model with DM interaction are asymmetrical.

DOI
10.1088/1612-202x/ab1015

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We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-1/21/21/2 XYXYXY model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.
Abstract Here we employ trace distance and bipartite correlations as the detectors for quantum phase transitions (QPTs). Their performances behaving in Ising spin chains with Dzyaloshinskii–Moriya (DM) interaction and an external transverse field are studied, respectively. Exploiting the quantum renormalization group method, all the detectors can effectively characterize the QPTs at the critical points. Moreover, the block–block correlations existing in the multipartite spin systems never violate the Bell inequality with the DM interaction, whereas they are enough to violate this inequality under the transverse field. Finally, we detail the nonanalytic and scaling behavior of the trace distance, which is tightly connected to the critical features of spin systems.
Abstract In this paper, by using the quantum renormalization-group method, we study the relation between total quantum coherence based on l 1 norm and quantum phase transition in the XXZ model with Dzyaloshinskii–Moriya (DM) interaction. Our findings reveal a distribution relation of quantum coherence in this model, i.e. the value of the quantum coherence of a three-site block state is equal to the sum of its reduced state coherence, and this characteristic can be generalized to a multipartite system. Meanwhile, because of favoring the alignment of spins, the anisotropy suppresses the quantum coherence; on the other hand, by creating the quantum fluctuations, the DM interaction can effectively enhance the value of quantum coherence. Additionally, after several iterations of the renormalization, quantum coherence of the whole block state can form two saturated values, which are related to two different phases: spin-fluid phase and Néel phase. Furthermore, we discover that the total quantum coherence of the block–block state obeys the nonanalytic and scaling properties with the quantum coherence exponent associated with correlation length.
We have studied the phase diagram and entanglement of the one-dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization-group (QRG) approach to get the stable fixed points, critical point, and the scaling of coupling constants. This model has two phases: antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes to infinity defines the critical point of the model. Moreover, we have analyzed the relevance of the entanglement in the model which allows us to shed insight on how the critical point is touched as the size of the system becomes large. Nonanalytic behavior of entanglement and finite-size scaling have been analyzed which is tightly connected to the critical properties of the model. It is also suggested that a spin-fluid phase has a chiral order in terms of spin operators which are defined by a nonlocal transformation.
We have studied the phase diagram of the one dimensional XXZ model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points, critical point and the scaling of coupling constants. This model has three phases, ferromagnetic, spin-fluid and Néel phases which are separated by a critical line which depends on the DM coupling constant. We have shown that the staggered magnetization is the order parameter of the system and investigated the influence of DM interaction on the chiral ordering as a helical magnetic order.
Three-Qubit Ground State and Thermal Entanglement of XXZXXZXXZ Model With Dzyaloshinskii-Moriya Interaction
We have studied the symmetric and non-symmetric pairwise ground state and thermal entanglement in three-qubit anisotropic Heisenberg (XXZ) and Ising in a magnetic field models and in the presence of Dzyaloshinskii-Moriya (DM) interaction. We have found that increasing of the DM interaction and magnetic field can enhance and reduce the entanglement of system. We have shown that the non-symmetric pairwise has higher value concurrence and critical temperature (above which the entanglement vanishes) than the symmetric pairwise. For negative anisotropy the non-symmetric entanglement is a monotonic function of DM interaction while for positive anisotropy it has a maximum versus DM parameter and vanishes for larger values of DM interaction. The conditions for the existence of thermal entanglement are discussed in details. The most remarkable result happens at zero temperature where 3-qubit ground state entanglement of the system (in spite of 2-qubit counterpart) shows the fingerprint of quantum phase transition for an infinite size system.