  We study a spin-1/2 XXZ model with a four-spin interaction on a two-leg
ladder. By means of effective field theory and matrix product state
calculations, we obtain rich ground-state phase diagrams that consist of eight
distinct gapped phases. Four of them exhibit spontaneous symmetry breaking with
either a magnetic or valence-bond-solid (VBS) long-range order. The other four
are featureless, i.e., the bulk ground state is unique and does not break any
symmetry. The featureless phases include the rung singlet (RS) and Haldane
phases as well as their variants, the RS* and Haldane* phases, in which twisted
singlet pairs are formed between the two legs. We argue and demonstrate that
Gaussian transitions with the central charge c=1 occur between the featureless
phases and between the ordered phases while Ising transitions with c=1/2 occur
between the featureless and ordered phases. The two types of transition lines
cross at the SU(2)-symmetric point, where the criticality is described by the
SU(2)_2 Wess-Zumino-Witten theory with c=3/2. The RS-Haldane* and RS*-Haldane
transitions give examples of topological phase transitions. Interestingly, the
RS* and Haldane* phases, which have highly anisotropic nature, appear even in
the vicinity of the isotropic case. We demonstrate that all the four
featureless phases are distinguished by topological indices in the presence of
certain symmetries.
