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Home  >  Transactions OF NAMP VOL1

5. Two Holes Dynamics in the Ising Antiferromagnetic Chains by S. Ehika and J.O.A. Idiodi Transactions of NAMP Volume 1, (November, 2015), pp 33 – 50
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The t-Jz model is the strongly anisotropic limit of the t-J model which captures some general properties of the doped antiferromagnets (AF). The absence of spin fluctuations simplifies the analytical treatment of this problem and makes it possible to visualize the independent effect of hole(s) on the antiferromagnet. This paper studies the dynamics of two holes on one dimensional Ising antiferromagnetic Mott insulator. The energy of the two holes for none zero exchange Jz is calculated using exact diagonalization method. Systems with Odd number of sites N up to nine are presented. The energy of the hole is found to increase slightly in the weak coupling regime (Jz/t<<1)  and sharply in the strong coupling regime (Jz/t<<1) . This increase in the energy of the holes is due to the magnetic energy cost incurred in creating a ferromagnetic bond or a string of flipped spins. Comparison with the result obtained for the single hole at finite   shows that the energy expended by a single hole in an Ising antiferromagnet is greater than that expended by two holes in the same background. In particular, it is observed that an increase in N increases the single hole energy slightly. On the other hand, an increase in N causes a decrease in the energy of two holes for finite  .  This means that two mobile holes in the bulk limit in one dimensional antiferromagnet can minimize their energy and so maintain a smooth coherent motion. The implication of this result for superconductivity of doped Mott insulators is discussed.

Keywords: Ising antiferromagnet, confinement,  bulk limit, exact diagonalization and hole pairing.