  In a one-dimensional (1D) superconductor, zero temperature quantum
fluctuations destroy phase coherence. Here we put forward a mechanism which can
restore phase coherence: power-law hopping. We study a 1D attractive-U Hubbard
model with power-law hopping by Abelian bosonization and density-matrix
renormalization group (DMRG) techniques. The parameter that controls the
hopping decay acts as the effective, non-integer spatial dimensionality
$d_{eff}$. For real-valued hopping amplitudes we identify analytically a range
of parameters for which power-law hopping suppress fluctuations and restore
superconducting long-range order for any $d_{eff} > 1$. A detailed DMRG
analysis fully supports these findings. These results are also of direct
relevance to quantum magnetism as our model can be mapped onto a S=1/2 XXZ
spin-chain with power-law decaying couplings, which can be studied
experimentally by cold ion-trap techniques.
