  We study theoretically the quantum phase transition from a metal to a
Wigner-Mott insulator at fractional commensurate filling on a two-leg ladder.
We show that a continuous transition out of a symmetry-preserving Luttinger
liquid metal is possible where the onset of insulating behavior is accompanied
by the breaking of the lattice translation symmetry. At fillings $\nu = 1/m$
per spin per unit cell, we find that the spin degrees of freedom also acquire a
gap at the Wigner-Mott transition for odd integer $m$. In contrast for even
integer $m$, the spin sector remains gapless and the resulting insulator is a
ladder analog of the two-dimensional spinon surface state. In both cases, a
charge neutral spinless mode remains gapless across the Wigner-Mott transition.
We discuss physical properties of these transitions, and comment on insights
obtained for thinking about continuous Wigner-Mott transitions in
two-dimensional systems which are being studied in moire materials.
