Cumulant expansion in the Holstein model: Spectral functions and mobility

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dc.citation.issue12
dc.citation.rankM22
dc.citation.spage125165
dc.citation.volume107
dc.contributor.authorMitrić, Petar
dc.contributor.authorJanković, Veljko
dc.contributor.authorVukmirović, Nenad
dc.contributor.authorTanasković, Darko
dc.date.accessioned2023-05-15T09:56:46Z
dc.date.available2023-05-15T09:56:46Z
dc.date.issued2023-05-30
dc.description.abstractWe examine the range of validity of the second-order cumulant expansion (CE) for the calculation of spectral functions, quasiparticle properties, and mobility of the Holstein polaron. We devise an efficient numerical implementation that allows us to make comparisons in a broad interval of temperature, electron-phonon coupling, and phonon frequency. For a benchmark, we use the dynamical mean-field theory which gives, as we have recently shown, rather accurate spectral functions in the whole parameter space, even in low dimensions. We find that in one dimension, the CE resolves well both the quasiparticle and the first satellite peak in a regime of intermediate coupling. At high temperatures, the charge mobility assumes a power law μ∝T−2 in the limit of weak coupling and μ∝T−3/2 for stronger coupling. We find that, for stronger coupling, the CE gives slightly better results than the self-consistent Migdal approximation (SCMA), while the one-shot Migdal approximation is appropriate only for a very weak electron-phonon interaction. We also analyze the atomic limit and the spectral sum rules. We derive an analytical expression for the moments in CE and find that they are exact up to the fourth order, as opposed to the SCMA where they are exact to the third order. Finally, we analyze the results in higher dimensions.
dc.identifier.doi10.1103/physrevb.107.125165
dc.identifier.issn2469-9950
dc.identifier.issn2469-9969
dc.identifier.scopus2-s2.0-85151342093
dc.identifier.urihttps://pub.ipb.ac.rs/handle/123456789/24
dc.language.isoen
dc.publisherAmerican Physical Society (APS)
dc.relation.ispartofPhysical Review B
dc.relation.ispartofabbrPhys. Rev. B
dc.rightsopenAccess
dc.titleCumulant expansion in the Holstein model: Spectral functions and mobility
dc.typejournal-article
dc.type.versionpublishedVersion
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