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.
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 University of British Columbia [UBC]
- 2 Leibniz-Institut für Festkörper- und Werkstoffforschung Dresden / Leibniz Institute for Solid State and Materials Research [IFW]
- Canada First Research Excellence Fund
- Max-Planck-Gesellschaft zur Förderung der Wissenschaften / Max Planck Society [MPG]
- Conseil de Recherches en Sciences Naturelles et en Génie / Natural Sciences and Engineering Research Council [NSERC / CRSNG]
- Stewart Blusson Quantum Matter Institute, University of British Columbia
- University of British Columbia
- 東京大学 / University of Tokyo [UT]