503 research outputs found
Decoherence in weak localization II: Bethe-Salpeter calculation of Cooperon
This is the second in a series of two papers (I and II) on the problem of
decoherence in weak localization. In paper I, we discussed how the Pauli
principle could be incorporated into an influence functional approach for
calculating the Cooperon propagator and the magnetoconductivity. In the present
paper II, we check and confirm the results so obtained by diagrammatically
setting up a Bethe-Salpeter equation for the Cooperon, which includes
self-energy and vertex terms on an equal footing and is free from both infrared
and ultraviolet divergencies. We then approximately solve this Bethe-Salpeter
equation by the Ansatz C(t) = C^0 (t) e^{-F(t)}, where the decay function F(t)
determines the decoherence rate. We show that in order to obtain a
divergence-free expression for the decay function F(t), it is sufficient to
calculate C^1 (t), the Cooperon in the position-time representation to first
order in the interaction. Paper II is independent of paper I and can be read
without detailed knowledge of the latter.Comment: 18 pages, 3 figures. This is the second of a series of two papers on
decoherence. The first introduces an influence functional approach, the
second obtains equivalent results using a diagrammatic Bethe-Salpeter
equation. For a concise summary of the main results and conclusions, see
Section II of the first pape
Matrix product state approach for a two-lead, multi-level Anderson impurity model
We exploit the common mathematical structure of the numerical renormalization
group and the density matrix renormalization group, namely, matrix product
states, to implement an efficient numerical treatment of a two-lead,
multi-level Anderson impurity model. By adopting a star-like geometry, where
each species (spin and lead) of conduction electrons is described by its own
Wilson chain, instead of using a single Wilson chain for all species together,
we achieve a very significant reduction in the numerical resources required to
obtain reliable results. We illustrate the power of this approach by
calculating ground state properties of a four-level quantum dot coupled to two
leads. The success of this proof-of-principle calculation suggests that the
star geometry constitutes a promising strategy for future calculations the
ground state properties of multi-band, multi-level quantum impurity models.
Moreover, we show that it is possible to find an "optimal" chain basis,
obtained via a unitary transformation (acting only on the index distinguishing
different Wilson chains), in which degrees of freedom on different Wilson
chains become effectively decoupled from each other further out on the Wilson
chains. This basis turns out to also diagonalize the model's chain-to-chain
scattering matrix. We demonstrate this for a spinless two-lead model,
presenting DMRG-results for the mutual information between two sites located
far apart on different Wilson chains, and NRG results with respect to the
scattering matrix.Comment: extended version, 11 pages, 12 figure
Low temperature dephasing saturation from elastic magnetic spin disorder and interactions
We treat the question of the low temperature behavior of the dephasing rate
of the electrons in the presence of elastic spin disorder scattering and
interactions. In the frame of a self-consistent diagrammatic treatment, we
obtain saturation of the dephasing rate in the limit of low temperature for
magnetic scattering, in agreement with the non-interacting case. The magnitude
of the dephasing rate is set by the strength of the magnetic scattering rate.
We discuss the agreement of our results with relevant experiments.Comment: This paper supersedes cond-mat/021022
Comment on "Theoretical analysis of the transmission phase shift of a quantum dot in the presence of Kondo correlations"
Recently, A. Jerez, P. Vitushinsky and M. Lavagna [Phys. Rev. Lett. 95,
127203 (2005)] claimed that the transmission phase through a quantum fot, as
measured via the Aharonov-Bohm interferometer, differs from the phase which
determines the corresponding conductance. Here we show that this claim is wrong
for the single level Anderson model, which is usually used to describe the
quantum dot. So far, there exists no derivation of this claim from any explicit
theoretical model.Comment: To appear as a Comment in PR
Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
We show how spectral functions for quantum impurity models can be calculated
very accurately using a complete set of ``discarded'' numerical renormalization
group eigenstates, recently introduced by Anders and Schiller. The only
approximation is to judiciously exploit energy scale separation. Our derivation
avoids both the overcounting ambiguities and the single-shell approximation for
the equilibrium density matrix prevalent in current methods, ensuring that
relevant sum rules hold rigorously and spectral features at energies below the
temperature can be described accurately.Comment: 4 pages + 1 page appendix, 2 figure
Dynamical conductance in the two-channel Kondo regime of a double dot system
We study finite-frequency transport properties of the double-dot system
recently constructed to observe the two-channel Kondo effect [R. M. Potok et
al., Nature 446, 167 (2007)]. We derive an analytical expression for the
frequency-dependent linear conductance of this device in the Kondo regime. We
show how the features characteristic of the 2-channel Kondo quantum critical
point emerge in this quantity, which we compute using the results of conformal
field theory as well as numerical renormalization group methods. We determine
the universal cross-over functions describing non-Fermi liquid vs. Fermi liquid
cross-overs and also investigate the effects of a finite magnetic field.Comment: 11 pages in PRB forma
Variational matrix product state approach to quantum impurity models
We present a unified framework for renormalization group methods, including
Wilson's numerical renormalization group (NRG) and White's density-matrix
renormalization group (DMRG), within the language of matrix product states.
This allows improvements over Wilson's NRG for quantum impurity models, as we
illustrate for the one-channel Kondo model. Moreover, we use a variational
method for evaluating Green's functions. The proposed method is more flexible
in its description of spectral properties at finite frequencies, opening the
way to time-dependent, out-of-equilibrium impurity problems. It also
substantially improves computational efficiency for one-channel impurity
problems, suggesting potentially \emph{linear} scaling of complexity for
-channel problems.Comment: revised version with application to Kondo model at large magnetic
field (5 pages, 2 figures
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