Influence Functional for Decoherence of Interacting Electrons in Disordered Conductors

We have rederived the controversial influence functional approach of Golubev and Zaikin (GZ) for interacting electrons in disordered metals in a way that allows us to show its equivalence, before disorder averaging, to diagrammatic Keldysh perturbation theory. By representing a certain Pauli factor (1-2 rho) occuring in GZ's effective action in the frequency domain (instead of the time domain, as GZ do), we also achieve a more accurate treatment of recoil effects. With this change, GZ's approach reproduces, in a remarkably simple way, the standard, generally accepted result for the decoherence rate. -- The main text and appendix A.1 to A.3 of the present paper have already been published previously; for convenience, they are included here again, together with five additional, lengthy appendices containing relevant technical details.Comment: Final version, as submitted to IJMPB. 106 pages, 11 figures. First 16 pages contain summary of main results. Appendix A summarizes key technical steps, with a new section A.4 on "Perturbative vs. Nonperturbative Methods". Appendix C.4 on thermal weighting has been extended to include discussion [see Eqs.(C.22-24)] of average energy of electron trajectorie

Bosonization for Beginners --- Refermionization for Experts

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, $\rho_{dos} (\omega)$, 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 $\rho_{dos}(\omega) \sim \omega$. 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 $e^{-i \Phi(x)}$ and the boson field $\Phi (x)$ itself.Comment: Revtex, 70 pages. Changes: Regarding the controversial tunneling density of states at an impurity in a g=1/2 Luttinger liquid, we (1) give a new, more explicit calculation, (2) show that contrary to recent suggestions (including our own), Oreg and Finkel'stein treat fermionic anticommutation relations CORRECTLY (see Appendix K), but (3) suggest that their MEAN-FIELD treatment of their Coulomb gas may not be sufficiently accurat

Poor man's derivation of the Bethe-Ansatz equations for the Dicke model

We present an elementary derivation of the exact solution (Bethe-Ansatz equations) of the Dicke model, using only commutation relations and an informed Ansatz for the structure of its eigenstates.Comment: 2 page

Multiloop functional renormalization group for general models

We present multiloop flow equations in the functional renormalization group (fRG) framework for the four-point vertex and self-energy, formulated for a general fermionic many-body problem. This generalizes the previously introduced vertex flow [F. B. Kugler and J. von Delft, Phys. Rev. Lett. 120, 057403 (2018)] and provides the necessary corrections to the self-energy flow in order to complete the derivative of all diagrams involved in the truncated fRG flow. Due to its iterative one-loop structure, the multiloop flow is well-suited for numerical algorithms, enabling improvement of many fRG computations. We demonstrate its equivalence to a solution of the (first-order) parquet equations in conjunction with the Schwinger-Dyson equation for the self-energy

Fermi-edge singularity and the functional renormalization group

We study the Fermi-edge singularity, describing the response of a degenerate electron system to optical excitation, in the framework of the functional renormalization group (fRG). Results for the (interband) particle-hole susceptibility from various implementations of fRG (one- and two- particle-irreducible, multi-channel Hubbard-Stratonovich, flowing susceptibility) are compared to the summation of all leading logarithmic (log) diagrams, achieved by a (first-order) solution of the parquet equations. For the (zero-dimensional) special case of the X-ray-edge singularity, we show that the leading log formula can be analytically reproduced in a consistent way from a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic structure, we show that this derivation relies on fortuitous partial cancellations special to the form of and accuracy applied to the X-ray-edge singularity and does not generalize