1998/05/21 by Jan von Delft, Herbert Schoeller · 1 voice · 2 citations
Physics and Astronomy · #cond-mat.str-el #cond-mat.mes-hall
paper · pdf · doi:10.1002/(sici)1521-3889(199811)7:4<225::aid-andp225>3.0.co;2-l
arxiv published 1998/05/21 · arxiv updated 1998/10/30
This tutorial gives an elementary and self-contained review of abelian bosonization in 1 dimension in a system of finite size L, following and simplifying Haldane's constructive approach. As a non-trivial application, we rigorously resolve (following Furusaki) a recent controversy regarding the tunneling density of states, ρdos (ω), at the site of an impurity in a Tomonaga-Luttinger liquid: we use finite-size refermionization to show exactly that for g=1/2 its asymptotic low-energy behavior is ρdos(ω) ∼ ω. This agrees with the results of Fabrizio & Gogolin and of Furusaki, but not with those of Oreg and Finkel'stein (probably because we capture effects not included in their mean-field treatment of the Coulomb gas that they obtained by an exact mapping; their treatment of anti-commutation relations in this mapping is correct, however, contrary to recent suggestions in the literature). --- The tutorial is addressed to readers unfamiliar with bosonization, or for those interested in seeing ``all the details'' explicitly; it requires knowledge of second quantization only, not of field theory. At the same time, we hope that experts too might find useful our explicit treatment of certain subtleties -- these include the proper treatment of the so-called Klein factors that act as fermion-number ladder operators (and also ensure the anti-commutation of different species of fermion fields), the retention of terms of order 1/L, and a novel, rigorous formulation of finite-size refermionization of both e-i Φ(x) and the boson field Φ(x) itself.