Interchain-coupling effect on the one-dimensional spin-1/2 antiferromagnetic Heisenberg model

Azzouz, Mohamed

doi:10.1103/physrevb.48.6136

Cited by 61 publications

(77 citation statements)

References 17 publications

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“…Moreover, the ordered moment size continuously decreases in the regime of extremely reduced ratio T N /J = 4 × 10 −3 ∼ 10 −2 . This suggests that the ordered moment vanishes smoothly in the R = J ′ /J → 0 limit, rather than maintaining a limiting size (dashed line in Fig.4) as has been proposed theoretically [28].…”

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confidence: 78%

Reduction of Ordered Moment and Néel Temperature of Quasi-One-Dimensional AntiferromagnetsSr2CuO3and
Kojima
¹
,
Fudamoto
²
,
Larkin
³

et al. 1997
Phys. Rev. Lett.
187
20
144
1
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We report elastic neutron diffraction and muon spin relaxation (µSR) measurements of the quasi one-dimensional antiferromagnets Sr2CuO3 and Ca2CuO3, which have extraordinarily reduced TN/J ratios.We observe almost resolution-limited antiferromagnetic Bragg reflections in Sr2CuO3 and obtain a reduced ordered moment size of ∼0.06µB. We find that the ratio of ordered moment size µ(Ca2CuO3)/µ(Sr2CuO3) = 1.5(1) roughly scales with their Néel temperatures, which suggests that the ordered moment size of quasi one-dimensional antiferromagnets decreases continuously in the limit of vanishing inter-chain interactions.PACS numbers: 76.75.+i, 75.25.+z, 75.10.Jm One-dimensional spin systems with antiferromagnetic interactions have received considerable attention because of their pronounced quantum mechanical effects. In the absence of inter-chain interactions, both integer and halfodd integer spin-chain systems have spin-singlet ground states, rather than an antiferromagnetically ordered Néel state [1][2][3]. Yet, for half odd-integer spin-chains, the spin-excitations are gap-less at momentum k = 0 and π [4]; this indicates that the ground state of a half-odd integer spin-chain is closer to the Néel ordered state than the integer spin systems, which have a so-called Haldane gap [3].Because of the gap-less feature of half-odd integer spinchains, one interesting question is whether the ground state is ordered or disordered when inter-chain interactions are introduced. Previously, it was proposed that there is a non-zero critical coupling ratio (J ′ /J = R c ), below which the system retains a singlet ground-state [5]. Recent renormalization group calculations however suggest that the ground state may depend on microscopic details of the model which describes the spin-spin interactions [6,7]. Numerical studies of the Heisenberg model suggested a vanishing critical coupling ratio (R c ∼ 0); namely, for infinitesimally small inter-chain couplings, half odd-integer spin-chains should exhibit Néel order [7].Experimentally, KCuF 3 is the most investigated quasione-dimensional S=1/2 antiferromagnet. Unfortunately, this material has relatively large coupling ratio R = J ′ /J ∼ 2 K/203 K = 1.0 × 10 −2 , as shown from neutron inelastic scattering measurements [8]. Probably reflecting the large coupling ratio R, the T N /J ratio (∼ 39 K/203 K = 0.2) and the ordered moment size (= 0.49(7)µ B [9]) were also found to be relatively large.To investigate the regime of the critical coupling ratio, model materials with smaller inter-chain couplings are needed; the quasi one-dimensional S=1/2 antiferromagnets Sr 2 CuO 3 and Ca 2 CuO 3 are suitable candidates. The intra-chain interaction (2J ∼ 2600 K) of these materials have been estimated from susceptibility [10,11] and infrared light absorption [12]. Néel ordering of these compounds was first observed in µSR measurements [13], with a significantly reduced T N /J ratio of ∼ 5 K/1300 K = 4 × 10 −3 for Sr 2 CuO 3 and T N /J ∼ 11 K/1300 K = 8 × 10 −3 for Ca 2 CuO 3 . Since T N /J is a measure of ...

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mentioning

confidence: 78%

Reduction of Ordered Moment and Néel Temperature of Quasi-One-Dimensional AntiferromagnetsSr2CuO3and
Kojima
¹
,
Fudamoto
²
,
Larkin
³

et al. 1997
Phys. Rev. Lett.
187
20
144
1
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“…In this work, we explicitly show the emergence of unpaired Majorana zero modes associated with the twist defects using two different approaches: 1) a generalized 2D Jordan-Wigner transformation [13][14][15] ; 2) a projective construction from a Majorana surface code model. In addition, we show that the parity operator of two unpaired Majorana modes is indeed the logical operator defined in the spin language, which can be used to manipulate the degenerate states of the corresponding twists.…”

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confidence: 99%

Demonstrating non-Abelian statistics of Majorana fermions using twist defects

2015

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We study the twist defects in the toric code model introduced by Bombin [Phys. Rev. Lett. 105, 030403 (2010)]. Using a generalized 2D Jordan-Wigner transformation and a projective construction, we show explicitly the twist defects carry unpaired Majorana zero modes. In addition, we propose a quantum non-demolition measurement scheme of the parity of Majorana modes. Such a scheme provides an alternative avenue to demonstrate the non-Abelian statistics of Majorana fermions. The braiding operation is simulated by a non-repetitive measurement-based approach which removes the uncertainty associated with forced measurements.

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“…Similar discussion was given in Ref. [16]. Then we go on to search for the value δ * which may be obtained from the condition ∂E GS /∂δ = 0, yielding the following equation:…”

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confidence: 99%

“…This method has been proved well for application to real materials [15,9]. For concreteness, the following formulas are adopted [16,17] …”

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confidence: 99%

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Spin-Peierls transition in an anisotropic two-dimensionalXYmodel

2001

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The two-dimensional Jordan-Wigner transformation is used to investigate the zero temperature spin-Peierls transition for an anisotropic two-dimensional XY model in adiabatic limit. The phase diagram between the dimerized (D) state and uniform (U) state is shown in the parameter space of dimensionless interchain coupling h (= J ⊥ /J) and spin-lattice coupling η. It is found that the spin-lattice coupling η must exceed some critical value η c in order to reach the D phase for any finite h. The dependence of η c on h is given by −1/ ln h for h → 0 and the transition between U and D phase is of first-order for at least h > 10 −3 .

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Interchain-coupling effect on the one-dimensional spin-1/2 antiferromagnetic Heisenberg model

Cited by 61 publications

References 17 publications

Reduction of Ordered Moment and Néel Temperature of Quasi-One-Dimensional AntiferromagnetsSr2CuO3and
Kojima
¹
,
Fudamoto
²
,
Larkin
³

et al. 1997
Phys. Rev. Lett.
187
20
144
1
View full text Add to dashboard Cite

Reduction of Ordered Moment and Néel Temperature of Quasi-One-Dimensional AntiferromagnetsSr2CuO3and
Kojima
¹
,
Fudamoto
²
,
Larkin
³

et al. 1997
Phys. Rev. Lett.
187
20
144
1
View full text Add to dashboard Cite

Demonstrating non-Abelian statistics of Majorana fermions using twist defects

Spin-Peierls transition in an anisotropic two-dimensionalXYmodel

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Interchain-coupling effect on the one-dimensional spin-1/2 antiferromagnetic Heisenberg model

Cited by 61 publications

References 17 publications

Reduction of Ordered Moment and Néel Temperature of Quasi-One-Dimensional AntiferromagnetsSr2CuO3andKojima1, Fudamoto2, Larkin3 et al. 1997Phys. Rev. Lett.187201441View full textAdd to dashboardCite

Reduction of Ordered Moment and Néel Temperature of Quasi-One-Dimensional AntiferromagnetsSr2CuO3andKojima1, Fudamoto2, Larkin3 et al. 1997Phys. Rev. Lett.187201441View full textAdd to dashboardCite

Demonstrating non-Abelian statistics of Majorana fermions using twist defects

Spin-Peierls transition in an anisotropic two-dimensionalXYmodel

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Product

Resources

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Reduction of Ordered Moment and Néel Temperature of Quasi-One-Dimensional AntiferromagnetsSr2CuO3and
Kojima
¹
,
Fudamoto
²
,
Larkin
³

et al. 1997
Phys. Rev. Lett.
187
20
144
1
View full text Add to dashboard Cite

Reduction of Ordered Moment and Néel Temperature of Quasi-One-Dimensional AntiferromagnetsSr2CuO3and
Kojima
¹
,
Fudamoto
²
,
Larkin
³

et al. 1997
Phys. Rev. Lett.
187
20
144
1
View full text Add to dashboard Cite