Hole Binding in a One-Dimensional Long-Range Spin ½ Interaction System

Using a Lanczos tridiagonal scheme to generate our basis, we study the novel spin chain Hamiltonian (expected to be in the same universality class as an XY Heisenberg system) given by H = ∑^N−1_j=1 ∑^N_k=1 j^(−1−p) [S⁽⁺⁾_k+j S⁽⁻⁾_k + S⁽⁻⁾_k+j S⁽⁺⁾_k + λ (S^(z)_k+j S^(z)_k + S^(z)_k S^(z)_k+j)]. By varying the initial (trial) state, we then study the hole binding energy, E_B = E₀ (two holes) + E₀ (no holes) − 2E₀ (one hole), as a function of hole separation, anisotropy parameter λ as well as the parameter p.