Title: Topological degeneracy and pairing in a one-dimensional gas of spinless Fermions,
Abstract: We revisit the low energy physics of one dimensional spinless fermion
liquids, showing that with sufficiently strong interactions the conventional
Luttinger liquid can give way to a strong pairing phase. While the density
fluctuations in both phases are described by a gapless Luttinger liquid, single
fermion excitations are gapped only in the strong pairing phase. Smooth spatial
Interfaces between the two phases lead to topological degeneracies in the
ground state and low energy phonon spectrum. Using a concrete microscopic
model, with both single particle and pair hopping, we show that the strong
pairing state is established through emergence of a new low energy fermionic
mode. We characterize the two phases with numerical calculations using the
density matrix renormalization group. In particular we find enhancement of the
central charge from $c=1$ in the two Luttinger liquid phases to $c=3/2$ at the
critical point, which gives direct evidence for an emergent critical Majorana
mode. Finally, we confirm the existence of topological degeneracies in the low
energy phonon spectrum, associated with spatial interfaces between the two
phases.