The present work reports an experimental observation of thermal entanglement in a clusterized spin chain formed in the compound
Na2Cu5Si4O14. The presence of entanglement was investigated through two measured quantities, an entanglement witness and the entanglement of formation, both derived from the magnetic susceptibility. It was found that pairwise entanglement exists below $\ensuremath{\sim}200\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Tripartite entanglement was also observed below $\ensuremath{\sim}240\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. A theoretical study of entanglement evolution as a function of applied field and temperature is also presented.
Detection of entangled states from experimental magnetic susceptibility is reported for an organic radical. The present system exemplifies an ideal spin ½ chain with full isotropy. Experimental susceptibility data are modelled by the formulation described by Bonner and Fisher. An explicit correlation is established between the molecular structure and the spin chain interaction. Using experimental magnetic susceptibility as entanglement witness, entanglement is observed to exist up to 28 K in the present system. Evolution of entanglement with magnetic field is also studied and a surface plot is generated, which clearly exhibits the variation of entanglement with magnetic field and temperature.
In this letter, we present an experimental observation of entanglement in a spin chain formed in the layered compound CaMn 2 Sb 2 . The presence of entanglement was investigated through a measurable quantity, the magnetic susceptibility. The entanglement witness obtained from the measurement is presented as a function of applied field for fixed temperatures. The presence of entanglement is observed even for reasonably high temperatures and applied fields. Since entanglement seems to occur naturally in this material, we suggest it to be used as an entanglement reservoir.
Entanglement has been extensively studied from the perspective of Quantum Information Processing for the last decade and various measures of entanglement, to quantify it are now available. Experimentally also it has been possible to measure entanglement in pure state, mostly in optics. However, in recent years there has been significant development in Quantum Condensed Matter systems, especially spin chains, where extraction of entanglement has been made possible through macroscopic witness operators like magnetic susceptibility. In this work, we have studied the magnetic properties of some spin chains, where the exchange interaction can be tuned by preparation technique and we have extracted a magnetic field and temperature dependence of entanglement from susceptibility and magnetization data taken at various temperatures and fields. The spin chains considered here fall in two categories, first one is an alternating dimer model and the second is an infinite spin chain. We have given the experimental plots of entanglement as a function of temperature and magnetic fields and compared them with the theoretical plots.
Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. We consider a spin tetramer, with spins of magnitude
21, in which the spins interact via nearest-neighbor, diagonal, and four-spin interactions of strength
J1,
J2, and
K, respectively. The ground- and thermal-state entanglement properties of the tetramer are calculated analytically in the various limiting cases. Both bipartite and multipartite entanglements are considered and a signature of the quantum phase transition (QPT), in terms of the entanglement ratio, is identified. The first-order QPT is accompanied by discontinuities in the nearest-neighbor and diagonal concurrences. The magnetic properties of a
S=21 antiferromagnetic polyoxovanadate compound V12 are well explained by tetramers, with
J2=0,
K=0, in which the spins interact via the isotropic Heisenberg exchange interaction Hamiltonian. Treating the magnetic susceptibility $\ensuremath{\chi}$ as an entanglement witness (EW), an estimate of the lower bound of the critical entanglement temperature
Tc below which entanglement is present in the experimental compound, is determined. Two other cases considered include the symmetric tetramer---i.e., tetrahedron
(J1=J2,K=0)---and the symmetric trimer. In both the cases, there is no entanglement between a pair of spins in the thermal state but multipartite entanglement is present. A second EW based on energy provides an estimate of the entanglement temperature
TE below which the thermal state is definitely entangled. This EW detects bipartite entanglement in the case of the tetramer describing a square of spins (the case of V12 ) and multipartite entanglement in the cases of the tetrahedron and symmetric trimer.
In this paper, we study three specific aspects of entanglement in small spin clusters. We first study the effect of inhomogeneous exchange coupling strengths on the entanglement properties of the
S=21 antiferromagnetic linear chain tetramer compound
NaCuAsO4. The entanglement gap temperature
TE is found to have a nonmonotonic dependence on the value of $\ensuremath{\alpha}$, the exchange coupling inhomogeneity parameter. We next determine the variation of
TE as a function of
S for a spin dimer, a trimer, and a tetrahedron. The temperature
TE is found to increase as a function of
S but the scaled entanglement gap temperature
tE goes to zero as
S becomes large. Last, we study a spin-1 dimer compound to illustrate the quantum complementarity relation. We show that in the experimentally realizable parameter region, magnetization and entanglement plateaus appear simultaneously at low temperatures as a function of the magnetic field. Also, the sharp increase in one quantity as a function of the magnetic field is accompanied by a sharp decrease in the other so that the quantum complementarity relation is not violated.