1996/12/03 by Ilya A. Gruzberg, N. Read, Subir Sachdev · 49 citations
Computer Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Computer science #Condensed matter physics #Conductance #Crossover #Enhanced Data Rates for GSM Evolution #Geometry #Mathematics #Network model #Physics #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum many-body systems #Scaling #Statistical physics #cond-mat.dis-nn #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.55.10593
published in Physical review. B, Condensed matter 55(16), 10593-10601 (American Physical Society) · 10 pages, REVTeX, 2 eps figures
arxiv created 1996/12/03 · openalex publication_date 1997/04/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider the directed network (DN) of edge states on the surface of a cylinder of length L and circumference C. By mapping it to a ferromagnetic superspin chain and using a scaling analysis we show its equivalence to a one-dimensional supersymmetric nonlinear \ensuremathσ model in the scaling limit for any value of the ratio L/C, except for short systems where L is less than of order C1/2. For the \ensuremathσ model, the universal crossover functions for the conductance and its variance have been determined previously. We also show that the DN model can be mapped directly onto the random matrix (Fokker-Planck) approach to disordered quasi-one-dimensional wires, which implies that the entire distribution of the conductance is the same as in the latter system for any value of L/C in the same scaling limit. The results of Chalker and Dohmen [Phys. Rev. Lett. 75, 4496 (1995)] are explained quantitatively.