Entanglement in a Dimerized Antiferromagnetic Heisenberg Chain

Hao, Xiang; Zhu, Shiqun

doi:10.1142/s0219749906002390

Cited by 4 publications

(2 citation statements)

References 34 publications

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“…An important magnetic quantum phenomenon related to this point is the spin-Peierls transition that occurs when a uniform antiferromagnetic chain becomes an alternating one because of the coupling between the vibrations (phonons) of the lattice and the exchange energy . Dimerization of spins leads to a modification of the excitation spectrum in the resulting alternating S = 1/2 Cu II antiferromagnetic chains, which have recently emerged as models for the study of the quantum entanglement phenomenon …”

Section: Introductionmentioning

confidence: 99%

Ligand Effects on the Structure and Magnetic Properties of Alternating Copper(II) Chains with 2,2′-Bipyrimidine- and Polymethyl-Substituted Pyrazolates as Bridging Ligands

et al. 2014

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A novel series of heteroleptic copper(II) compounds of formulas {[Cu2(μ-H2O)(μ-pz)2(μ-bpm)(ClO4)(H2O)]ClO4·2H2O}n (1), {[Cu2(μ-H2O)(μ-3-Mepz)2(μ-bpm)](ClO4)2·2H2O}n (2), and {[Cu2(μ-OH)(μ-3,5-Me2pz)(μ-bpm)(H-3,5-Me2pz)2](ClO4)2}n (3) [bpm = 2,2'-bipyrimidine, Hpz = pyrazole, H-3-Mepz = 3-methylpyrazole, and H-3,5-Me2pz = 3,5-dimethylpyrazole] have been synthesized and structurally characterized by X-ray diffraction methods. The crystal structures of 1 and 2 consist of copper(II) chains with regular alternating bpm and bis(pyrazolate)(aqua) bridges, whereas that of 3 is made up of copper(II) chains with regular alternating bpm and (pyrazolate)(hydroxo) bridges. The copper centers are six- (1) or five-coordinate (2) in axially elongated, octahedral (1) or square-pyramidal (2) environments in 1 and 2, whereas they are five-coordinate in distorted trigonal-bipyramidal surroundings in 3. The values of the copper-copper separations across the bpm/pyrazolate bridges are 5.5442(7)/3.3131(6) (1), 5.538(1)/3.235(1) (2), and 5.7673(7)/3.3220(6) Å (3). The magnetic properties of 1-3 have been investigated in the temperature range of 25-300 K. The analysis of their magnetic susceptibility data through the isotropic Hamiltonian for an alternating antiferromagnetic copper(II) chain model [H = -J∑i=1-n/2 (S2i·S2i-1 + αS2i·S2i+1), with α = J'/J and Si = SCu = 1/2] reveals the presence of a strong to moderate antiferromagnetic coupling through the bis(pyrazolate)(aqua) [-J = 217 (1) and 215 cm(-1) (2)] and (pyrazolate)(hydroxo) bridges [-J = 153 cm(-1) (3)], respectively, whereas a strong to weak antiferromagnetic coupling occurs through the bis-bidentate bpm [-J' = 211 (1), 213 (2), and 44 cm(-1) (3)]. A simple orbital analysis of the magnetic exchange interaction within the bpm- and pyrazolate-bridged dicopper(II) fragments of 1-3 visualizes the σ-type pathways involving the (dx(2)-y(2)) (1 and 2) or d(z(2)) (3) magnetic orbitals on each metal ion, which account for the variation of the magnetic properties in these three novel examples of one-dimensional copper(II) compounds with regular alternating intrachain antiferromagnetic interactions.

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Section: Introductionmentioning

confidence: 99%

Ligand Effects on the Structure and Magnetic Properties of Alternating Copper(II) Chains with 2,2′-Bipyrimidine- and Polymethyl-Substituted Pyrazolates as Bridging Ligands

et al. 2014

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“…Entanglement for the dimerized chain has been discussed in Refs. [29,30]. In order to evaluate the Bell correlations and then to investigate the monogamy bound (2), it is convenient to rewrite the eigenvalues u and u ′ defined in Eq.…”

Section: Qpts Correlations and Chsh Inequality -mentioning

confidence: 99%

Nonviolation of Bell’s inequality in translation invariant systems

Oliveira

Saguia

Sarandy

2013

EPL

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The nature of quantum correlations in strongly correlated systems has been a subject of intense research. In particular, it has been realized that entanglement and quantum discord are present at quantum phase transitions and are able to characterize them. Surprisingly, it has been shown for a number of different systems that qubit pairwise states, even when highly entangled, do not violate Bell's inequalities, being in this sense local. Here we show that such a local character of quantum correlations traces back to the the monogamy trade-off obeyed by bipartite Bell correlations, being in fact general for translation invariant systems. We illustrate this result in a quantum spin chain with a soft breaking of translation symmetry. In addition, we provide an extension of the monogamy inequality to the N -qubit scenario, showing that the bound increases with N and providing examples of its saturation through uniformly generated random pure states.

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Reduced-fidelity approach for quantum phase transitions in spin-12dimerized Heisenberg chains

Xiong

Sun

et al. 2009

Phys. Rev. B

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Entanglement in a Dimerized Antiferromagnetic Heisenberg Chain

Cited by 4 publications

References 34 publications

Ligand Effects on the Structure and Magnetic Properties of Alternating Copper(II) Chains with 2,2′-Bipyrimidine- and Polymethyl-Substituted Pyrazolates as Bridging Ligands

Ligand Effects on the Structure and Magnetic Properties of Alternating Copper(II) Chains with 2,2′-Bipyrimidine- and Polymethyl-Substituted Pyrazolates as Bridging Ligands

Nonviolation of Bell’s inequality in translation invariant systems

Reduced-fidelity approach for quantum phase transitions in spin-12dimerized Heisenberg chains

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