The even-odd effect in short antiferromagnetic Heisenberg chains

Abstract

Motivated by recent experiments on chemically synthesized magnetic molecular chains we investigate the lowest lying energy band of short spin-$s$ antiferromagnetic Heisenberg chains focusing on effects of open boundaries. By numerical diagonalization we find that the Landé pattern in the energy levels, i.e. E(S) \propto S(S+1) for total spin S, known from e.g. ring-shaped nanomagnets, can be recovered in odd-membered chains while strong deviations are found for the lowest excitations in chains with an even number of sites. This particular even-odd effect in the short Heisenberg chains cannot be explained by simple effective Hamiltonians and symmetry arguments. We go beyond these approaches, taking into account quantum fluctuations by means of a path integral description and the valence bond basis, but the resulting quantum edge-spin picture which is known to work well for long chains does not agree with the numerical results for short chains and cannot explain the even-odd effect. Instead, by analyzing also the classical chain model, we show that spatial fluctuations dominate the physical behavior in short chains, with length N < exp(πs), for any spin s. Such short chains are found to display a unique behavior, which is not related to the thermodynamic limit and cannot be described well by theories developed for this regime.

25 pages, 16 figures

References in corpus (35)

• Exact spectra, spin susceptibilities and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice
• Magnetic Cluster Excitations
• Large-Scale Numerical Evidence for Bose Condensation in the S=1 Antiferromagnetic Chain in a Strong Field
• Impurities in S=1/2 Heisenberg Antiferromagnetic Chains: Consequences for Neutron Scattering and Knight Shift
• Rotational modes in molecular magnets with antiferromagnetic Heisenberg exchange
• Macroscopic Quantum Coherence in Molecular Magnets
• Meron-Cluster Simulation of the $\theta$-Vacuum in the 2-d $O(3)$-Model
• The Antiferromagnetic Heisenberg Model on Clusters with Icosahedral Symmetry
• Magnetic Properties of Undoped $C_{60}$
• Elementary excitations in the cyclic molecular nanomagnet Cr8
• Equal Time Correlations in Haldane Gap Antiferromagnets
• Some formal results for the valence bond basis
• Quantum rotational band model for the Heisenberg molecular magnet Mo72Fe30
• Thermodynamics and Spin Tunneling Dynamics in Ferric Wheels with Excess Spin
• Magnetic excitations in {Mo72Fe30}
• Spin- and charge-density oscillations in spin chains and quantum wires
• Edge states in Open Antiferromagnetic Heisenberg Chains
• Neel order in doped quasi one-dimensional antiferromagnets
• Discrete antiferromagnetic spin-wave excitations in the giant ferric wheel Fe18
• Magnetization in Molecular Iron Rings
• Thermodynamics of impurities in the anisotropic Heisenberg spin-1/2 chain
• Universal alternating order around impurities in antiferromagnets
• E-band excitations in the magnetic Keplerate molecule Fe30
• Quantum dynamics of the Neel vector in the antiferromagnetic molecular wheel CsFe8
• Topological effects at short antiferromagnetic Heisenberg chains
• Knight shifts around vacancies in the 2D Heisenberg model
• Singular field response and singular screening of vacancies in antiferromagnets
• Standing Spin Waves in an Antiferromagnetic Molecular Cr6 Horseshoe
• Spin 3/2 dimer model
• Interaction effects between impurities in low dimensional spin-1/2 antiferromagnets
• Even-odd effects in finite Heisenberg spin chains
• Lattice vs. continuum theory of the periodic Heisenberg chain
• Quantum tunneling of the Neel vector in antiferromagnetic [3 x 3] grid molecules
• Spin wave calculation of the field-dependent magnetization pattern around an impurity in Heisenberg antiferromagnets
• Quantum Nonlinear Sigma Model for Arbitrary Spin Heisenberg Antiferromagnets

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• Boundary-induced spin density waves in linear Heisenberg antiferromagnetic spin chains with $\mathbf{S}\ge 1$
• Antiferromagnetic molecular nanomagnets with odd-numbered coupled spins
• Magnetization distribution in a spin ladder-shaped quantum nanomagnet
• $\mathbf{\Delta }$S${}^z$=2 quantum magnetization discontinuities proportional in number to the spin s in C${}_{60}$: Origin and the role of symmetry
• Long-lived Neel states in antiferromagnetic quantum spin chains with strong uniaxial anisotropy for atomic-scale antiferromagnetic spintronics
• Parity-dependent phase diagrams in spin-cluster two-leg ladders
• Promising regimes for the observation of topological degeneracy in spin chains
• Investigation of the spin dynamics of quantum spin dimers with Dzyaloshinsky-Moriya interaction
• A systematic approach to determine the spectral characteristics of molecular magnets