Dzyaloshinskii-Moriya interaction and anisotropy effects on the entanglement of the Heisenberg model

Kargarian, Mehdi; Jafari, R.; Langari, A.

doi:10.1103/physreva.79.042319

Cited by 154 publications

(113 citation statements)

References 38 publications

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“…To slightly generalize it, let us add a Dzyaloshinskii-Moriya (DM) interaction 20 and on every link we consider the operators,…”

Section: Limiting Cases: Xy and Xxz Chainsmentioning

confidence: 99%

“…The field theory value of ∆ c is πJ/2 while the exact solution gives ∆ c = J 13 . The XXZ limit that would correspond to massless Thirring model has been analyzed from spin systems and entanglement points of view 20,22 where the critical value is obtained to be ∆ c = J. In the λ = 0 situation a Dzyaloshinskii-Moriya interaction of strength D can be added to the above XXZ form which results in a gapless line separating the spin-fluid phase from ferromagnetic and/or anti-ferromagnetic Ising phases depending on the sign of ∆ 20 .…”

Section: Introductionmentioning

confidence: 99%

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Exact phase boundaries and topological phase transitions of the XYZ spin chain

Jafari¹

2017

Phys. Rev. E

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Within the block spin renormalization group we are able to construct the exact phase diagram of the XYZ spin chain. First we identify the Ising order alongx orŷ as attractive renormalization group fixed points of the Kitaev chain. Then in a global phase space composed of the anisotropy λ of the XY interaction and the coupling ∆ of the ∆σ z σ z interaction we find that the above fixed points remain attractive in the two dimesional parameter space. We therefore classify the gapped phases of the XYZ spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain which in turn is characterized by winding number ±1 depending whether the Ising order parameter is alongx orŷ directions; or (2) attracted to the Mott phases of the underlying Jordan-Wigner fermions which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the XYZ model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the XYZ model justifies why our analytical solution of the three-site problem which is at the core of the renormalization group treatment is able to produce the exact phase diagram of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the Mott-Ising phase is entitled to host apprpriate form of zero modes. We further observe that the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

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“…To slightly generalize it, let us add a Dzyaloshinskii-Moriya (DM) interaction 20 and on every link we consider the operators,…”

Section: Limiting Cases: Xy and Xxz Chainsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact phase boundaries and topological phase transitions of the XYZ spin chain

Jafari¹

2017

Phys. Rev. E

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“…The pairwise entanglement of the system is also discussed by means of quantum renormalization group (QRG) method [16,17]. Very recently, the spin−1/2 Ising and Heisenberg models are studied by using the same method by a group of Iran and found that the systems exist QPT [18][19][20][21]. It is also shown that the nonanalytic behavior of the entanglement and the scaling behaviors closing to the quantum critical point are obtained.…”

Section: Introductionmentioning

confidence: 99%

Entanglement and quantum phase transition in the one-dimensional anisotropicXYmodel

Liu

Kong

2011

Phys. Rev. A

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In this paper the entanglement and quantum phase transition of the anisotropic s = 1/2 XY model are studied by using the quantum renormalization group method. By solving the renormalization equations, we get the trivial fixed point and the untrivial fixed point which correspond to the phase of the system and the critical point, respectively. Then the concurrence between two blocks are calculated and it is found that when the number of the iterations of the renormalziation trends infinity, the concurrence develops two staturated values which are associated with two different phases, i.e., Ising-like and spin-fluid phases. We also investigate the first derivative of the concurrence, and find that there exists non-analytic behaviors at the quantum critical point, which directly associate with the divergence of the correlation length. Further insight, the scaling behaviors of the system are analyzed, it is shown that how the maximum value of the first derivative of the concurrence reaches the infinity and how the critical point is touched as the size of the system becomes large.

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“…The Dzyaloshinsky-Moriya exchange interaction describes superexchange between the interacting spins, and is known to generate many dramatical features [18][19][20][21][22]. It is found that DM interaction can excite entanglement and teleportation fidelity.…”

Section: Introductionmentioning

confidence: 99%

Quantum Correlation in Three-Qubit Heisenberg Model with Dzyaloshinskii—Moriya Interaction

Tian¹,

Yan²,

Qin³

2012

Commun. Theor. Phys.

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We investigate the pairwise thermal quantum discord in a three-qubit XXZ model with Dzyaloshinskii-Moriya (DM) interaction. We find that the DM interaction can increase quantum discord to a fixed value in the antiferromagnetic system, but decreases quantum discord to a minimum first, then increases it to a fixed value in the ferromagnetic system. Abrupt change of quantum discord is observed, which indicates the abrupt change of groundstate. Dynamics of pairwise thermal quantum discord is also considered. We show that thermal discord vanishes in asymptotic limit regardless of its initial values, while thermal entanglement suddenly disappears at finite time.

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Dzyaloshinskii-Moriya interaction and anisotropy effects on the entanglement of the Heisenberg model

Cited by 154 publications

References 38 publications

Exact phase boundaries and topological phase transitions of the XYZ spin chain

Exact phase boundaries and topological phase transitions of the XYZ spin chain

Entanglement and quantum phase transition in the one-dimensional anisotropicXYmodel

Quantum Correlation in Three-Qubit Heisenberg Model with Dzyaloshinskii—Moriya Interaction

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