2007/10/18 by Yuji Hamamoto, Ken‐Ichiro Imura, Ken-Ichiro Imura +1
Physics and Astronomy · #Charge (physics) #Condensed matter physics #Luttinger liquid #Phase (matter) #Phase diagram #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Renormalization group #Scattering #Spin (aerodynamics) #Theoretical and Computational Physics #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.77.165402
published as Phys. Rev. B 77 (2008) 165402 · 10 pages, 8 figures
arxiv created 2007/10/18 · openalex publication_date 2008/04/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The single impurity problem in a spinful Tomonaga--Luttinger liquid is studied numerically using path-integral Monte Carlo methods. The advantage of our approach is that the system allows for extensive analyses of charge and spin conductance in the nonperturbative regime. By closely examining the behavior of conductances at low temperatures, in the presence of a finite backward scattering barrier due to the impurity, we identified four distinct phases characterized by either perfect transmission or reflection of charge and spin channels. Our phase diagram for an intermediate scattering strength is consistent with the standard perturbative renormalization group (RG) analysis in the limit of weak and strong backward scatterings, in the sense that all our phase boundaries interpolate the two limiting cases. Further investigations show, however, that precise location and form of our phase boundaries are not trivially explained by the standard RG analysis, e.g., some part of the phase diagram looks much similar to the weak backscattering limit, whereas some other part is clearly derived from the opposite limit. In order to give a more intuitive interpretation of such behaviors, we also reconsidered our impurity problem from the viewpoint of a quantum Brownian motion picture.