Oreg and Finkel'stein Reply:

Oreg, Yuval; Finkel’stein, Alexander M.

doi:10.1103/physrevlett.78.4528

Cited by 60 publications

(119 citation statements)

References 7 publications

(7 reference statements)

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“…The exponent n governing the low-energy behavior of r dos w $ w nÀ1 as w 3 0, was the subject of a recent controversy: Without impurities, it is known that n free g 1aga2. In the presence of an impurity, Oreg and Finkel'stein (OF) [21] found n 1a2g, using an exact mapping to a Coulomb gas problem, which they treated in a mean-field approximation; this would imply that n`n free , i.e. r dos w is enhanced, and actually diverges for w 3 0 if g b 1a2.…”

Section: B Application To Tomonaga-luttinger Liquid With Impuritymentioning

confidence: 99%

“…We use the same notation Ã Ã Ã Ã for boson as for fermion normal ordering, because a boson normal-ordered expression is automatically fermion normal ordered, as follows by takingÑ 0 in Eq. (21). Conversely, if a product purely of boson operators is fermion normal-ordered, i.e.…”

Section: D Bosonic Ground States Jñimentioning

confidence: 99%

“…(Leipzig) 7 (1998) 4 5 Above, we took Eqs. (24) to (26) as the defining relations for F h and F y h , and derived (30) to (32) from them. Note that if instead Eqs.…”

Section: Boson Fields ± Definition and Propertiesmentioning

confidence: 99%

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Bosonization for beginners - refermionization for experts

Delft¹,

Schoeller²

1998

Ann. Phys.

521

765

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This tutorial review gives an elementary and self-contained derivation of the standard identities (ψη(x) ∼ Fηe −iφη (x) , etc.) for 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, ρ dos (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 ρ dos (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 with little or no prior knowledge of bosonization, who are interested in seeing "all the details" explicitly; it is written at the level of beginning graduate students, requiring only knowledge of second quantization, but not of field theory (which is not needed here). At the same time, we hope that experts too might find useful our explicit treatment of certain subtleties that can often be swept under the rug, but are crucial for some applications, such as the calculation of ρ dos (ω)-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 F e −iΦ(x) and the boson field Φ(x) itself. Changes relative to first version of cond-mat/9805275: We have substantially revised our discussion of the controversy regarding the tunneling density of states ρ dos at the site of an impurity in a Luttinger liquid, with regard to the following points: (1) In a new Appendix K, we confirm explicitly that Oreg and Finkel'stein's treatment of fermionic anti-commutation relations is correct, contrary to recent suggestions (including our own). (2) To try to understand why their result for ρ dos differs from that of Fabrizio & Gogolin, Furusaki and (for g=1/2) ourselves, we make a new suggestion in Sections 1.B and 10.D: this is probably because of effects not captured by their mean-field treatment of their Coulomb gas. (3) In Sections 10.C and 10.D we have replaced the first version of our calculation of ρ dos by a more explicit one (the result is unchanged), in which we refermionize not only the exponential e iΦ but, for the first time, also the field Φ itself (Section 10.C.4); this allows us to calculate various correlation functions involving Φ explicitly in terms of fermion operators (a new Appendix J contains several detailed examples, and a new Figure 4 showing the corresponding Feynman diagrams).

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Section: B Application To Tomonaga-luttinger Liquid With Impuritymentioning

confidence: 99%

Section: D Bosonic Ground States Jñimentioning

confidence: 99%

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Bosonization for beginners - refermionization for experts

Delft¹,

Schoeller²

1998

Ann. Phys.

521

765

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“…Therefore, usual perturbation expansion treatment of this term becomes impossible, and one needs to use renormalization group equations to compute some physical quantities. However, with different perturbation methods, one may obtain different results because of divergence of the renormalized backward scattering potential, so it is not surprising that there are debates on the lowenergy behavior of electron density of states, 5,14,20,21 the contribution of the backward scattering to the exponent of Fermi-edge singularity of x-ray absorption, [1][2][3][4]14,[22][23][24] and so on.…”

Section: Introductionmentioning

confidence: 99%

Influence of backward scattering on correlation exponents in a one-dimensional system

Liu

2000

Phys. Rev. B

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Using bosonization and phase shift representation, we rigorously treat backward scattering of electrons on an impurity in a one-dimensional interacting spinless electronic system, and demonstrate that correlation exponents of the system depend on a phase shift induced by the backward scattering, and usual exponent duality between ultraviolet and infrared fixed points comes from the phase shift dependence of the correlation exponents.

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“…In fact this result has been considerably debated [20,23,24]; compare also [25], as well as the detailed presentation by von Delft and Schoeller [26]. 3 …”

Section: Dos Boundary Exponentmentioning

confidence: 98%

Quasiclassical theory of electronic transport in mesoscopic systems: Luttinger liquids revisited

Eckern¹,

Schwab

2007

Physica Status Solidi (b)

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The method of the quasiclassical Green's function is used to determine the equilibrium properties of onedimensional (1D) interacting Fermi systems, in particular, the bulk and the local (near a hard wall) density of states. While this is a novel approach to 1D systems, our findings do agree with standard results for Luttinger liquids obtained with the bosonization method. Analogies to the so-called P (E) theory of tunneling through ultrasmall junctions are pointed out and are exploited. Further applications of the Green's function method for 1D systems are discussed.

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Oreg and Finkel'stein Reply:

Cited by 60 publications

References 7 publications

Bosonization for beginners - refermionization for experts

Bosonization for beginners - refermionization for experts

Influence of backward scattering on correlation exponents in a one-dimensional system

Quasiclassical theory of electronic transport in mesoscopic systems: Luttinger liquids revisited

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