Hole Binding in the One-Dimensional Dimerized Heisenberg Model with Next-Nearest-Neighbor Interactions

Here we wish to study the 1D dimerized Heisenberg model given by H=∑_k J₁[1-(-1)^kδ]{S⁽⁺⁾_k+1S^(–)_k+2S^(z)_k+1S^(z)_k}+∑_k J₂{S⁽⁺⁾_k+2S^(–)_k+2S^(z)_k+2S^(z)_k}, where S^(±) are the usual spin ½ stepping operators and δ is the dimerization parameter. In particular, we shall use a Lanczos formulation to study the binding energy of two holes, Ε_B = Ε₀ wo holes) + Ε₀ (no holes) – 2Ε₀ (one hole), where we have varied the ground-state configuration so that we may evaluate Ε_B as a function of hole separation.