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Chinese Physics

Entanglement in the supermolecular dimer [Mn4]2

Xu Chang-Tan, Gang Chen, He Ming-Ming, Liang Ju-Qing

Published Nov 2, 2006• 4 citations
Publisher

Abstract

This paper investigates the entanglement in the supermolecular dimer [Mn 4 ] 2 consisting of a pair of single molecular magnets with antiferromagnetic exchange-coupling J . The conventional von Neumann entropy as a function of the exchange-coupling is calculated explicitly for all eigenstates with the quantum number range from M = M 1 + M 2 = −9 to 0. It is shown that the von Neumann entropy is not a monotonic function of the coupling strength. However, it is significant that the entropy of entanglement has the maximum values and the minimum values for most eigenstates, which is extremely useful in the quantum computing. It also presents the time-evolution of entanglement from various initial states. The results are useful in the design of devices based on the entanglement of two molecular magnets.

DOI
10.1088/1009-1963/15/12/010

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This paper investigates the entanglement in the supermolecular dimer [Mn 4 ] 2 consisting of a pair of single molecular magnets with antiferromagnetic exchange-coupling J . The conventional von Neumann entropy as a function of the exchange-coupling is calculated explicitly for all eigenstates with the quantum number range from M = M 1 + M 2 = −9 to 0. It is shown that the von Neumann entropy is not a monotonic function of the coupling strength. However, it is significant that the entropy of entanglement has the maximum values and the minimum values for most eigenstates, which is extremely useful in the quantum computing. It also presents the time-evolution of entanglement from various initial states. The results are useful in the design of devices based on the entanglement of two molecular magnets.
A new family of the supramolecular antiferromagnetically exchange-coupled dimer of single-molecules magnets, [Mn 4 ] 2 , really behave as a quantum mechanical coupled system and can be used for quantum computation [Tiron et al (2003) Phys. Rev. Lett . 91 227203]. We study the time evolution of [Mn 4 ] 2 dimer interacting with an injected electron by solving the time-dependent Schrödinger equations. We find that the variations of [Mn 4 ] 2 dimer magnetization and the electron spin crucially depend on the exchange interaction strength. Time evolution of the entanglement between the injected electron and supramolecular dimer [Mn 4 ] 2 is evaluated. It is observed that entanglement oscillates in time and is closely related to the spin variation of injected electron. From these characteristics the technique for the reversing and read-out of supramolecular dimer [Mn 4 ] 2 spin states is suggested.
In the present work, we investigate the quantum thermal entanglement in molecular magnets composed of dimers of spin S , using an Entanglement Witness built from measurements of magnetic susceptibility. An entanglement temperature, T e , is then obtained for some values of spin S . From this, it is shown that T e is proportional to the intradimer exchange interaction J and that entanglement appears only for antiferromagnetic coupling. The results are compared to experiments carried on three isostructural materials: KNaMSi 4 O 10 (M=Mn, Fe or Cu).
Advances in quantum computing technology have been made in recent years due to the evolution of spin clusters. Recent studies have tended towards spin cluster subgeometries to understand more complex structures better. These molecular magnets provide a multitude of phenomena via exchange interactions that allow for advancements in spintronics and other magnetic system applications due to the possibility of increasing speed, data storage, memory, and stability of quantum computing systems. Using the Heisenberg spin–spin exchange Hamiltonian and exact diagonalization, we examine the evolution of quantum energy levels and thermodynamic properties for various spin configurations and exchange interactions. The XXYY quantum spin tetramer considered in this study consists of two coupled dimers with exchange interactions α1J and α1′J and a dimer–dimer exchange interaction α2J. By varying spin values and interaction strengths, we determine the exact energy eigenstates that are used to determine closed-form analytic solutions for the heat capacity and magnetic susceptibility of the system and further analyze the evolution of the properties of the system based on the parameter values chosen. Furthermore, this study shows that the Schottky anomaly shifts towards zero as the ground-state of the system approaches a quantum phase transition between spin states. Additionally, we investigate the development of phase transitions produced by the convergence of the Schottky anomaly with both variable exchange interactions and external magnetic field.
In this Brief Report the properties of both dynamical and static entanglement in the integrable quantum dimer are studied in terms of the reduced-density linear entropy and von Neumann entropy with various coupling parameters, total boson numbers, and initial states. The mean entanglement, which is defined to be averaged over time, is used to describe the influence of the classical separatrix on the behavior of entanglement. It is shown that the mean entanglement exhibits a maximum near the position of the corresponding classical separatrix energy and that the static entanglement of the state with the largest eigenvalue of the quantum spectrum displays a maximum near the bifurcation point. For weak coupling and larger total boson number the maximum entanglement state is exactly at the position of the classical separatrix and bifurcation. In strong coupling all initial states have nearly the same mean entanglement.
"We use the density matrix renormalization group to calculate the von Neumann block entropy in the Kondo necklace model. We have included two anisotropies: η in the exchange interaction between conduction spins, and ∆ in the coupling between localized and conduction spins. Calculating the energy gap for the one-dimensional model at zero temperature, it was obtained that when η > 0, a quantum phase transition between Kondo singlet and antiferomagnetic states for finite couplings occurs, and as ∆ increases the Kondo singlet phase is favoured. Now we observe that the quantum critical points of the model can be identified by a maximum of the von Neumann block entropy, so entanglement measures can be useful for determining the phase diagram of the anisotropic Kondo necklace model."
In this work, we explore the dynamics of entanglement of an isolated quantum system consisting of two time-dependent, coupled harmonic oscillators. Through the use of a numerical method that relies on the estimation of the system's Wigner representation by a specific Gaussian function, we investigate the time evolution of the entanglement entropy after an instant quench in the inherent parameters of the system. Besides, from the comparison of the results obtained from the analytical expression for the time-dependent von Neumann entropy with the numerically computed entropy data, the effectiveness of the numerical method is tested for a variety of angular frequency combinations. Also, we analyze how the entropy of entanglement change as a function of time.