  We study a spin-1/2 system with Heisenberg plus ring exchanges on a four-leg
triangular ladder using the density matrix renormalization group and Gutzwiller
variational wave functions. Near an isotropic lattice regime, for moderate to
large ring exchanges we find a spin Bose-metal phase with a spinon Fermi sea
consisting of three partially filled bands. Going away from the triangular
towards the square lattice regime, we find a staggered dimer phase with dimers
in the transverse direction, while for small ring exchanges the system is in a
featureless rung phase. We also discuss parent states and a possible phase
diagram in two dimensions.
