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Magnetic Resonance in Solids. Electronic Journal

Entanglement in One-Dimensional Open Chains of Spins 1/2 with XY-Hamiltonian

Serge I. Doronin, Edward B. Fel’dman, Alexey N. Pyrkov

Published Jan 1, 2006• 0 citations
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•Jan 1, 1999•0 citations
We present rigorous topological order which emerges in a one-dimensional spin-orbital model due to the ring topology. Although this model with SU(2) spin and XY orbital interactions is known to exactly separate spins from orbitals by means of a unitary transformation on the open chain, we find that they are not quite independent when the chain is closed, and the spins form two half-rings carrying opposite quasimomenta. We show that on changing the topology from an open to a periodic chain, the degeneracy of the ground state is partially lifted while the low-energy excitations have a quadratic dispersion as a function of the total quasimomentum. This novel type of topological order which emerges from changing the topology from an open to a periodic chain is reminiscent of the infinite-U Hubbard chain.
A method for exactly diagonalizing the XY Hamiltonian of an alternating open chain of spins s = 1/2 has been proposed on the basis of the Jordan-Wigner transformation and analysis of the dynamics of spinless fermions. The multiple-quantum spin dynamics of alternating open chains at high temperatures has been analyzed and the intensities of multiple-quantum coherences have been calculated. The problem of the transfer of a quantum state from one end of the alternating chain to the other is studied. It has been shown that the ideal transfer of qubits is possible in alternating chains with a larger number of spins than that in homogeneous chains.