Short-range antiferromagnetic correlations are known to open a spin
gap in the repulsive Hubbard model on ladders with
\boldsymbol{M}𝐌
legs, when \boldsymbol{M}𝐌
is even. We show that the spin gap originates from the formation of
correlated pairs of electrons with opposite spin, captured by the hidden
ordering of a spin-parity operator. Since both spin gap and parity
vanish in the two-dimensional limit, we introduce the fractional
generalization of spin parity and prove that it remains finite in the
thermodynamic limit. Our results are based upon variational wave
functions and Monte Carlo calculations: performing a finite size-scaling
analysis with growing \boldsymbol{M}𝐌,
we show that the doping region where the parity is finite coincides with
the range in which superconductivity is observed in two spatial
dimensions. Our observations support the idea that superconductivity
emerges out of spin gapped phases on ladders, driven by a spin-pairing
mechanism, in which the ordering is conveniently captured by the
finiteness of the fractional spin-parity operator.
Spin gap in low-dimensional Mott insulators with orbital degeneracy