  We define a new class of "diagonal" t-J ladders rotated by $\pi$/4 relative
to the canonical lattice directions of the square lattice, and study it using
density matrix renormalization group (DMRG). Here, we focus on the two-leg
cylinder with a doped hole concentration near x = 1/4. At exactly x = 1/4, the
system forms a period 4 charge density wave (CDW) and exhibits spin-charge
separation. Slightly away from 1/4 doping we observe several topologically
distinct types of solitons with well defined fractionalized quantum numbers.
Remarkably, given the absence of any obvious small parameter, the effective
masses of the emergent solitons differ by several orders of magnitude.
