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arXiv:1208.3997 · Physical Review B

Towards the chemical tuning of entanglement in molecular nanomagnets

Ilaria Siloi, Filippo Troiani

Published Dec 6, 2012• 19 citations
arXivHTMLPDF

Abstract

Antiferromagnetic spin rings represent prototypical realizations of highly correlated, low-dimensional systems. Here we theoretically show how the introduction of magnetic defects by controlled chemical substitutions results in a strong spatial modulation of spin-pair entanglement within each ring. Entanglement between local degrees of freedom (individual spins) and collective ones (total ring spins) are shown to coexist in exchange-coupled ring dimers, as can be deduced from general symmetry arguments. We verify the persistence of these features at finite temperatures, and discuss them in terms of experimentally accessible observables.

DOI
10.1103/physrevb.86.224404

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he multiqubit entangled states are coherently controlled in the quantum spin systems composed of N+1N+1N+1 interacting antiferromagnetic molecular rings. The tunable intermolecular couplings arise from the local exchange interactions between electron spins of NNN circumjacent magnets and those of one central molecular ring. The quantum dynamics of such system is analytically deduced by the effective spin hamiltonian with anisotropic Heisenberg couplings. It is found that entangled WWW states can be generated with a high precision under the circumstance of quantum fluctuations. The multiqubit entangled state is also transferred from some molecular rings to others by the selection of intermolecular couplings.
Entanglement between individual spins can be detected by using thermodynamics quantities as entanglement witnesses. This applies to collective spins also, provided that their internal degrees of freedom are frozen, as in the limit of weakly coupled nanomagnets. Here, we extend such approach to the detection of entanglement between subsystems of a spin cluster, beyond such weak-coupling limit. The resulting inequalities are violated in spin clusters with different geometries, thus allowing the detection of zero- and finite-temperature entanglement. Under relevant and experimentally verifiable conditions, all the required expectation values can be traced back to correlation functions of individual spins, which are now made selectively available by four-dimensional inelastic neutron scattering.
We address the characterization of molecular nanomagnets at the quantum level and analyze the performance of local measurements in estimating the physical parameters in their spin Hamiltonians. To this aim, we compute key quantities in quantum estimation theory, such as the classical and the quantum Fisher information, in the prototypical case of a heterometallic antiferromagnetic ring. We show that local measurements, performed only on a portion of the molecule, allow a precise estimate of the parameters related to both magnetic defects and avoided level crossings.
We investigate pairwise correlation properties of the ground state (GS) of finite antiferromagnetic (AFM) spin chains described by the Heisenberg model. The exchange coupling is restricted to nearest neighbor spins, and is constant J0J_0J0​ except for a pair of neighboring sites, where the coupling J1J_1J1​ may vary. We identify a rich variety of possible behaviors for different measures of pairwise (quantum and classical) correlations and entanglement in the GS of such spin chain. Varying a single coupling affects the degree of correlation between all spin pairs, indicating possible control over such correlations by tuning J1J_1J1​. We also show that a class of two spin states constitutes exact spin realizations of Werner states (WS). Apart from the basic and theoretical aspects, this opens concrete alternatives for experimentally probing non-classical correlations in condensed matter systems, as well as for experimental realizations of a WS via a single tunable exchange coupling in a AFM chain.
The multiple entangled states are controlled in the spin quantum systems composed of N+1 interacting antifer-romagnetic molecular rings.The tunable intermolecular couplings arise from the exchange interactions between electron spins of N circumjacent magnets and those of a central molecular ring.The quantum dynamics of such a system is deduced through the analysis of the effective spin hamiltonian with anisotropic Heisenberg couplings.It is found that an entangled W state can be generated precisely under the circumstance of quantum fluctuations.The multiple entangled state can also be transferred from some molecular rings to others by the manipulation of intermolecular couplings
One-dimensional (1D) magnetic systems offer rich phenomena in the quantum limit, proving more chemically accessible than zero-dimensional or higher-dimensional frameworks. Single-walled carbon nanotubes (SWCNT) have recently been used to encapsulate trimetric nickel(II) acetylacetonate [Nanoscale, 2019, 11, 10615–10621]. Here, we investigate the magnetization on spin chains based on nickel trimers by Matrix Product State (MPS) simulations. Our findings reveal plateaus in the exchange/magnetic-field phase diagram for three coupling configurations, showcasing effective dimeric and trimeric spin-ordering with similar or staggered entanglement across chains. These ordered states allow the qubit-like tuning of specific local magnetic moments, exhibiting disengagement or uniform coupling in entanglement plateaus. This behavior is consistent with the experimental transition from frustrated (3D) to non-frustrated (1D) molecules, corresponding to large and smaller SWCNT diameters. Our study offers insights into the potential of 1D-confined trimers for quantum computation, extending beyond the confinement of trimetric nickel-based molecules in one dimension.