967 research outputs found
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
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 , 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, , 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
. 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 and the boson field 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
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
Multiloop functional renormalization group that sums up all parquet diagrams
We present a multiloop flow equation for the four-point vertex in the
functional renormalization group (fRG) framework. The multiloop flow consists
of successive one-loop calculations and sums up all parquet diagrams to
arbitrary order. This provides substantial improvement of fRG computations for
the four-point vertex and, consequently, the self-energy. Using the X-ray-edge
singularity as an example, we show that solving the multiloop fRG flow is
equivalent to solving the (first-order) parquet equations and illustrate this
with numerical results
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