Phase diagram and entanglement of the Ising model with Dzyaloshinskii-Moriya interaction

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

doi:10.1103/physrevb.78.214414

Cited by 159 publications

(105 citation statements)

References 40 publications

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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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Section: Introductionmentioning

confidence: 99%

Entanglement and quantum phase transition in the one-dimensional anisotropicXYmodel

Liu

Kong

2011

Phys. Rev. A

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“…Although the presence of bond alternation breaks the translation invariance of the Hamiltonian it does not change the symmetry of the ground state which has already been spontaneously broken due to antiferromagnetic long range order. A comparison of our results with 13 concludes that the bond alternation does not change the universality class of the model as far as λ = 1.…”

Section: Summary and Discussionmentioning

confidence: 92%

Quantum critical phase diagram of bond alternating Ising model with Dzyaloshinskii–Moriya interaction: Signature of ground state fidelity

Amiri¹,

Langari²

2013

Physica Status Solidi (b)

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We present the zero temperature phase diagram of the bond alternating Ising chain in the presence of Dzyaloshinskii-Moriya interaction. An abrupt change in ground state fidelity is a signature of quantum phase transition. We obtain the renormalization of fidelity in terms of quantum renormalization group without the need to know the ground state. We calculate the fidelity susceptibility and its scaling behavior close to quantum critical point (QCP) to find the critical exponent which governs the divergence of correlation length. The model consists of a long range antiferromagnetic order with nonzero staggered magnetization which is separated from a helical ordered phase at QCP. Our results state that the critical exponent is independent of the bond alternation parameter (λ) while the maximum attainable helical order depends on λ.

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“…In the absence of the LF, the ground state phase diagram of the model is known [27][28][29] . The spectrum of the model for −D < J ≤ D is gapless and the system is in the so-called Luttinger-liquid (LL) phase with a power-law decay of correlations.…”

Section: The Modelmentioning

confidence: 99%

Quantum correlations in the 1D spin-1/2 Ising model with added Dzyaloshinskii–Moriya interaction

Soltani

Vahedi

Mahdavifar

2014

Physica A: Statistical Mechanics and its Applications

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We have considered the 1D spin-1/2 Ising model with added Dzyaloshinskii-Moriya (DM) interaction and presence of a uniform magnetic field. Using the mean-field fermionization approach the energy spectrum in an infinite chain is obtained. The quantum discord (QD) and concurrence between nearest neighbor (NN) spins at finite temperature are specified as a function of mean-field order parameters. A comparison between concurrence and QD is done and differences are obtained. The macroscopic thermodynamical witness is also used to detect quantum entanglement region in solids within our model. We believe our results are useful in the field of the quantum information processing.

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Phase diagram and entanglement of the Ising model with Dzyaloshinskii-Moriya interaction

Cited by 159 publications

References 40 publications

Entanglement and quantum phase transition in the one-dimensional anisotropicXYmodel

Entanglement and quantum phase transition in the one-dimensional anisotropicXYmodel

Quantum critical phase diagram of bond alternating Ising model with Dzyaloshinskii–Moriya interaction: Signature of ground state fidelity

Quantum correlations in the 1D spin-1/2 Ising model with added Dzyaloshinskii–Moriya interaction

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