Restoring phase coherence in a one-dimensional superconductor using power-law electron hopping

2012/12/31 by Alejandro M. Lobos, Masaki Tezuka, Antonio M. García-García +1 · 10 citations
Mathematics · Physics and Astronomy · #Coherence (philosophical gambling strategy) #Condensed matter physics #Electron #Mathematics #Phase (matter) #Phase coherence #Physics #Physics of Superconductivity and Magnetism #Power law #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Statistical physics #Superconductivity #cond-mat.str-el #cond-mat.supr-con

paper · pdf · doi:10.1103/physrevb.88.134506

published in Physical Review B 88(13) (American Physical Society) · 8 pages, 2 figures. New version with new figures, new references, clarified discussion on the variational method and an Appendix for details

arxiv created 2013/07/24 · openalex publication_date 2013/10/08 · arxiv updated 2013/10/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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 using Abelian bosonization and density-matrix renormalization group (DMRG) techniques. The parameter that controls the hopping decay acts as the effective, noninteger spatial dimensionality d_eff. For real-valued hopping amplitudes we identify analytically a range of parameters for which power-law hopping suppresses fluctuations and restores superconducting long-range order for any d_eff>1, at zero temperature. 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 an S=1/2 XXZ spin chain with power-law decaying couplings, which can be studied experimentally with cold-ion-trap techniques.

Citations

• Existence of Long-Range Order in One and Two Dimensions
• Quantum Fluctuations in Thin Superconducting Wires of Finite Length
• Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models
• Density-matrix algorithms for quantum renormalization groups
• Existence of a phase-transition in a one-dimensional Ising ferromagnet
• Open Luttinger Liquids
• The phase transition in the one-dimensional Ising Model with 1/r 2 interaction energy
• The density-matrix renormalization group in the age of matrix product states
• Superconductor-to-insulator transition in linear arrays of Josephson junctions capacitively coupled to metallic films