Stripes in the Ising limit of models for the cuprates

The hole-doped standard and extended $t-J$ models on ladders with anisotropic Heisenberg interactions are studied computationally in the interval $0.0<~\lambda <~1.0$ $(\lambda =0,$ Ising; $\lambda =1,$ Heisenberg) at small $J/t.\mathrm{}$ It is shown that the approximately half-doped stripes recently discussed at $\lambda =1\mathrm{}$ survive in the anisotropic case $(\lambda <1.0),$ particularly in the “extended” model. Due to the absence of spin fluctuations in the Ising limit and working in the rung basis, a simple picture emerges in which the stripe structure can be mostly constructed from the solution of the $t-J$ model on chains. A comparison of results in the range $0.0<~\lambda <~1.0$ suggests that this picture is valid up to the Heisenberg limit.