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Electron addition spectral functions of low-density polaron liquids

by Alberto Nocera, Mona Berciu

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Submission summary

Authors (as registered SciPost users): Alberto Nocera
Submission information
Preprint Link: scipost_202307_00023v1  (pdf)
Date accepted: 2023-07-31
Date submitted: 2023-07-18 04:35
Submitted by: Nocera, Alberto
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


Spectral functions are important quantities that contain a wealth of information about the quasiparticles of a system, and that can also be measured experimentally. For systems with electron-phonon coupling, good approximations for the spectral function are available only in the Migdal limit (at Fermi energies much larger than the typical phonon frequency, $E_F\gg \Omega$, requiring a large carrier concentration $x$) and in the single polaron limit (at $x=0$). Here we show that the region with $x\ll 1$ ($E_F <\Omega$) can also be reliably investigated with the Momentum Average (MA) variational approximation, which essentially describes the formation of a polaron above an inert Fermi sea. Specifically, we show that for the one-dimensional spinless Holstein model, the MA spectral functions compare favorably with those calculated using variationally exact density matrix renormalization group simulations (DMRG) evaluated directly in frequency-space, so long as $x<0.1$ and the adiabaticity ratio $\Omega/t>0.5$. Unlike in the Migdal limit, here 'polaronic physics' emerges already at moderate couplings. The relevance of these results for a spinful low-$x$ metal is also discussed.

Published as SciPost Phys. 15, 110 (2023)

Author comments upon resubmission

We thank the Referees for their positive evaluations and for suggesting ways to further improve our presentation. We address these in detail below. For ease of reading, the changes in the manuscript are indicated in blue, as are our replies to the Referees’ questions, below. We believe that we have addressed all suggestions requested by the Referees by adding a new figure (Fig 4) and several clarifications in our manuscript. We hope that our work will now be accepted for publication.

Sincerely yours,
Alberto Nocera and Mona Berciu

List of changes

Summary of Changes
1. We added Figure 4 showing momentum distribution functions calculated with DMRG.
2. We provided line cuts comparisons between MA and DMRG. In our opinion these do
not add new information, however we are happy to include them in the manuscript if
the Referee(s) request it.
3. We modified the text to make it more clear that the MA estimates of the effective
masses have already been published.

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