Breakdown of the Migdal-Eliashberg theory for electron-phonon systems. Role of polarons/bi-polarons
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| Format: | Preprint |
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2026
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| _version_ | 1866908981055717376 |
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| author | Chubukov, Andrey Esterlis, Ilya Abanov, Artem Prokof'ev, Nikolay |
| author_facet | Chubukov, Andrey Esterlis, Ilya Abanov, Artem Prokof'ev, Nikolay |
| contents | The Migdal-Eliashberg theory (MET) describes electrons interacting with phonons in the adiabatic limit when the phonon Debye frequency is much smaller than the Fermi energy. A conventional belief is that MET holds even at strong coupling, when electron self-energy is large, and breaks down only near the point where the dressed phonon spectrum softens to near zero. We analyze numerically and analytically a different option -- collapse to a polaronic/bipolaronic ground state. The last scenario has never been analyzed in precise quantitative terms for a generic electron density. Using variational considerations, we establish rigorous upper bounds on the coupling $λ$, at which a FL state transforms into the bipolaron/polaron state. We show that at small and near-maximum densities, this happens well before a dressed phonon softens. This is true both in 2D and 3D systems; in the latter the upper bound on $λ$ tends to zero in the limit of small or near-full density. We present analytical reasoning for this behavior based on hints extracted from exact diagrammatic treatment of the on-site Holstein model for the spin polarized case and argue that polarons are produced by fermions with energies comparable to the bandwidth; i.e., polaron formation is outside the realm of MET. Closer to half-filling, the leading instability upon increasing $λ$ is towards a charge-density-wave state (CDW), and there exists a strong coupling regime of MET near this instability, while the polaron/bipolaron state develops at larger $λ$ out of a CDW-ordered state and inherits a CDW order over some range of coupling. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_14294 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Breakdown of the Migdal-Eliashberg theory for electron-phonon systems. Role of polarons/bi-polarons Chubukov, Andrey Esterlis, Ilya Abanov, Artem Prokof'ev, Nikolay Strongly Correlated Electrons The Migdal-Eliashberg theory (MET) describes electrons interacting with phonons in the adiabatic limit when the phonon Debye frequency is much smaller than the Fermi energy. A conventional belief is that MET holds even at strong coupling, when electron self-energy is large, and breaks down only near the point where the dressed phonon spectrum softens to near zero. We analyze numerically and analytically a different option -- collapse to a polaronic/bipolaronic ground state. The last scenario has never been analyzed in precise quantitative terms for a generic electron density. Using variational considerations, we establish rigorous upper bounds on the coupling $λ$, at which a FL state transforms into the bipolaron/polaron state. We show that at small and near-maximum densities, this happens well before a dressed phonon softens. This is true both in 2D and 3D systems; in the latter the upper bound on $λ$ tends to zero in the limit of small or near-full density. We present analytical reasoning for this behavior based on hints extracted from exact diagrammatic treatment of the on-site Holstein model for the spin polarized case and argue that polarons are produced by fermions with energies comparable to the bandwidth; i.e., polaron formation is outside the realm of MET. Closer to half-filling, the leading instability upon increasing $λ$ is towards a charge-density-wave state (CDW), and there exists a strong coupling regime of MET near this instability, while the polaron/bipolaron state develops at larger $λ$ out of a CDW-ordered state and inherits a CDW order over some range of coupling. |
| title | Breakdown of the Migdal-Eliashberg theory for electron-phonon systems. Role of polarons/bi-polarons |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2604.14294 |