We derive a Hamiltonian for a two-leg ladder which included an arbitrary number of charge and spin interactions which must be weak but are otherwise of arbitrary strength. To illustrate the Hamiltonian we consider two examples and use a renormalization-group technique to evaluate the ground-state phases.
Bunder, J. E. & Lin, H. (2009). Generic short-range interactions in two-leg ladders. Physical Review B (Condensed Matter and Materials Physics), 79 045132-1-045132-11.