Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical renormalization group study of the symmetric Anderson-Holstein
  model: phonon and electron spectral functions   We study the symmetric Anderson-Holstein (AH) model at zero temperature with
Wilson's numerical renormalization group (NRG) technique to study the interplay
between the electron-electron and electron-phonon interactions. An improved
method for calculating the phonon propagator using the NRG technique is
presented, which turns out to be more accurate and reliable than the previous
works in that it calculates the phonon renormalization explicitly and satisfies
the boson sum rule better. The method is applied to calculate the renormalized
phonon propagators along with the electron propagators as the onsite Coulomb
repulsion $U$ and electron-phonon coupling constant $g$ are varied. As $g$ is
increased, the phonon mode is successively renormalized, and for $g \gtrsim
g_{co}$ crosses over to the regime where the mode splits into two components,
one of which approaches back to the bare frequency and the other develops into
a soft mode. The initial renormalization of the phonon mode, as $g$ is
increased from 0, depends on $U$ and the hybridization $\Delta$; it gets
softened (hardened) for $U \gtrsim (\lesssim) U_s (\Delta)$. Correlated with
the emergence of the soft mode is the central peak of the electron spectral
function severely suppressed. These NRG calculations will be compared with the
standard Green's function results for the weak coupling regime to understand
the phonon renormalization and soft mode.

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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: math
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th