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

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.

8 pages, 2 figures. New version with new figures, new references, clarified discussion on the variational method and an Appendix for details

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Cited by in corpus (9)

• Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems
• Kaleidoscope of quantum phases in a long-range interacting spin-1 chain
• Superconductivity in repulsively interacting fermions on a diamond chain: flat-band induced pairing
• Quantum Quenches in the Luttinger model and its close relatives
• Out-of-equilibrium phase diagram of long-range superconductors
• Global critical temperature in inhomogeneous superconductors induced by multifractality
• Detection of unbroken phase of non-Hermitian system via Hermitian factorization surface
• Destruction of Long-range Order by Quenching the Hopping Range in One Dimension
• Effect of long-range interactions on multipartite entanglement in Heisenberg chains