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

Soltani, M. R.; Vahedi, Javad; Mahdavifar, S.

doi:10.1016/j.physa.2014.08.017

Cited by 20 publications

(8 citation statements)

References 41 publications

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“…In this literature, we introduce S ± as S ± = S x ± iS y . By applying the Jordan-Wigner transformation, the reduced density matrix will be written as [56][57][58][59] …”

Section: Quantum Correlationsmentioning

confidence: 99%

Magnetic quantum correlations in the one-dimensional transverse-field XXZ model

Mahdavifar¹,

Jafari²

2017

Phys. Rev. A

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One-dimensional spin-1/2 systems are well-known candidates to study the quantum correlations between particles. In the condensed matter physics, studies often are restricted to the 1st neighbor particles. In this work, we consider the 1D XXZ model in a transverse magnetic field (TF) which is not integrable except at specific points. Analytical expressions for quantum correlations (entanglement and quantum discord) between spin pairs at any distance are obtained for both zero and finite temperature, using an analytical approach proposed by Caux et al. [PRB 68, 134431 (2003)]. We compare the efficiency of the QD with respect to the entanglement in the detection of critical points (CPs) as the neighboring spin pairs go farther than the next nearest neighbors. In the absence of the TF and at zero temperature, we show that the QD for spin pairs farther than the 2nd neighbors is able to capture the critical points while the pairwise entanglement is absent. In contrast to the pairwise entanglement, two-site quantum discord is effectively long-range in the critical regimes where it decays algebraically with the distance between pairs. We also show that the thermal quantum discord between neighbor spins possesses strong distinctive behavior at the critical point that can be seen at finite temperature and, therefore, spotlights the critical point while the entanglement fails in this task.

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“…In this literature, we introduce S ± as S ± = S x ± iS y . By applying the Jordan-Wigner transformation, the reduced density matrix will be written as [56][57][58][59] …”

Section: Quantum Correlationsmentioning

confidence: 99%

Magnetic quantum correlations in the one-dimensional transverse-field XXZ model

Mahdavifar¹,

Jafari²

2017

Phys. Rev. A

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“…[40] The zero-temperature effect of the DM interaction on the entanglement in the 1D spin-1/2 Heisenberg model has also been investigated extensively. [41,42] Our numerical analysis is based on exact diagonalizations of Hamiltonians of spin-1∕2 chain with up to N = 18 sites. The CC and QD are obtained for nearest-neighbor pairs of spins in all the eigenstates in a fixed magnetization sector, in the integrable and chaotic regimes.…”

Section: Introductionmentioning

confidence: 99%

“…[ 40 ] The zero‐temperature effect of the DM interaction on the entanglement in the 1D spin‐1/2 Heisenberg model has also been investigated extensively. [ 41,42 ]…”

Section: Introductionmentioning

confidence: 99%

Concurrence and Quantum Discord in the Eigenstates of Chaotic and Integrable Spin Chains

et al. 2020

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There has been some substantial research about the connections between quantum chaos and quantum correlations in many-body systems. This paper discusses a specific aspect of correlations in chaotic spin models, through concurrence (CC) and quantum discord (QD). Numerical results obtained in the quantum chaos regime and in the integrable regime of spin-1/2 chains are compared. The CC and QD between nearest-neighbor pairs of spins are calculated for all energy eigenstates. The results show that, depending on whether the system is in a chaotic or integrable regime, the distribution of CC and QD are markedly different. On the other hand, in the integrable regime, states with the largest CC and QD are found in the middle of the spectrum, in the chaotic regime, the states with the strongest correlations are found at low and high energies at the edges of spectrum. Finite-size effects are analyzed, and some of the results are discussed in the light of the eigenstate thermalization hypothesis.

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“…1 (b)). In the last years this technique has been successfully used to study the GS phase diagram of the Heisenberg 69,70 and Ising spin chains [71][72][73][74][75][76][77] .…”

Section: Introductionmentioning

confidence: 99%

Quantum correlations in the spin-1/2 Heisenberg XXZ chain with modulated Dzyaloshinskii-Moriya interaction

Fumani

Beradze

Nemati

et al. 2020

Preprint

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We study a one-dimensional spin-1/2 XXZ Heisenberg model with alternating Dzyaloshinskii-Moriya interaction, using the numerical Lanczos method. Recently, the ground state (GS) phase diagram of this model has been established using the bosonization approach and extensive density matrix renormalization group computations. Four quantum phases -saturated ferromagnetic (FM), Luttinger liquid (LL), and two (C1 and C2) gapped phases with composite structure of GS order, characterized by the coexistence of long-range alternating dimer, chirality and antiferromagnetic order have been identified. Here we reexamine the same problem using the exact diagonalization Lanczos method for chains up to N = 26 sites and explicitly detect positions of quantum critical points (QCP) by investigating the quantum correlations as the entanglement and the quantum discord (QD). It is shown that the entanglement quantified by concurrence and the first derivative of the QD are able to reveal besides the standard FM QCP also the Berezinskii-Kosterlitz-Thouless (BKT) phase transition point between the LL and the gapped C1 phase and the Ising type critical point separating the C1 and C2 phases.

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

Cited by 20 publications

References 41 publications

Magnetic quantum correlations in the one-dimensional transverse-field XXZ model

Magnetic quantum correlations in the one-dimensional transverse-field XXZ model

Concurrence and Quantum Discord in the Eigenstates of Chaotic and Integrable Spin Chains

Quantum correlations in the spin-1/2 Heisenberg XXZ chain with modulated Dzyaloshinskii-Moriya interaction

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