Phase coherence in one-dimensional superconductivity by power-law hopping

TL;DR

This paper demonstrates that power-law hopping in a 1D superconductor can restore phase coherence and long-range order, challenging the conventional understanding of quantum fluctuations destroying superconductivity in one dimension.

Contribution

It introduces a mechanism using power-law hopping to restore superconducting order in 1D systems and provides analytical and numerical evidence supporting this.

Findings

Power-law hopping suppresses quantum fluctuations in 1D superconductors.

Restoration of long-range superconducting order for effective dimensionality greater than one.

Relevance to quantum magnetism and experimental realization with cold ion traps.

Abstract

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.