  Interacting fermionic ladders are important platforms to study quantum phases
of matter, such as different types of Mott insulators. In particular, the
D-Mott and S-Mott states hold pre-formed fermion pairs and become
paired-fermion liquids upon doping (d-wave and s-wave, respectively). We show
that the D-Mott and S-Mott phases are in fact two facets of the same
topological phase and that the transition between them is terminable. These
results provide a quantum analog of the well-known terminable liquid-to-gas
transition. However, the phenomenology we uncover is even richer, as in
contrast to the former, the order of the transition can be tuned by the
interactions from continuous to first-order. The findings are based on
numerical results using the variational uniform matrix-product state (VUMPS)
formalism for infinite systems, and the density-matrix renormalization group
(DMRG) algorithm for finite systems. This is complemented by analytical
field-theoretical explanations. In particular, we present an effective theory
to explain the change of transition order, which is potentially applicable to a
broad range of other systems. The role of symmetries and edge states are
briefly discussed.
