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Home  >  Transactions OF NAMP VOL1

4.Single Hole Dynamics in One Dimensional Quantum Antiferromagnet. by S. Ehika and J.O.A. Idiodi Transactions of NAMP Volume 1, (November, 2015), pp 21 – 32
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Exact diagonalization (ED) study on 1D cuprates doped with a single hole and modelled by the more realistic  t - J  Hamiltonian is carried out on finite one dimensional systems up to eight sites. The energy expended by the hole is found to decrease with the system size. This observation is in contrast to the motion of a hole in Ising antiferromagnetic chain, where the hole energy increases slightly with system size.  This lowering of the energy of the hole gives a coherent propagation to the hole, at least in the weak coupling regime (J<<1).  Evidently, this reduction in the energy of the hole is due to the quantum spin fluctuation term in the t - J   model that helps to “heal” pair of flipped spins created by hole dynamics. In the strong coupling regime, the energy of the hole is positive at  J=0.8 and J=1.0   for four and eight sites respectively. Hence, in this regime, the hole shows more tendencies to be confined for shorter lengths than longer lengths of propagation. This is an exact opposite to what is observed for the case of the Ising model, and is also in stark contrast to the behaviour of a hole in two dimensional antiferromagnet, where confinement grows with the distance travelled by the hole. This deconfinement of hole in one dimensional quantum antiferromagnet lends credence to both theoretical and experimental reports of spin charge separation in one dimensional Mott Insulator.

Keywords: Quantum antiferromagnet, hole confinement, thermodynamic limit, exact diagonalization and spin-charge separation.