Abstract
We derive a Hamiltonian for a two-leg ladder which includes an arbitrary number of charge and spin interactions which must be weak but are otherwise of arbitrary strength. To illustrate this Hamiltonian we consider two examples and use a renormalization-group technique to evaluate the ground-state phases. The first example is a two-leg ladder with zigzagged legs. We find that increasing the number of interactions in such a two-leg ladder may result in a richer phase diagram, particularly at half-filling where a few exotic phases are possible when the number of interactions are large and the angle of the zigzag is small. In the second example we determine under which conditions a two-leg ladder at quarter-filling is able to support a Tomanaga-Luttinger liquid phase. We show that this is only possible when the spin interactions across the rungs are ferromagnetic. In both examples we focus on lithium purple bronze, a two-leg ladder with zigzagged legs which is thought to support a Tomanaga-Luttinger liquid phase. © 2009 The American Physical Society.