Spectral properties of a narrow-band Anderson model
We consider single-particle spectra of a symmetric narrow-band Anderson impurity model, where the host bandwidth D is small compared to the hybridization strength Δ0. Simple second-order perturbation theory (2PT) in U is found to produce a rich spectral structure that leads to rather good agreement...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2001
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| _version_ | 1797060320524500992 |
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| author | Schafer, S Logan, D |
| author_facet | Schafer, S Logan, D |
| author_sort | Schafer, S |
| collection | OXFORD |
| description | We consider single-particle spectra of a symmetric narrow-band Anderson impurity model, where the host bandwidth D is small compared to the hybridization strength Δ0. Simple second-order perturbation theory (2PT) in U is found to produce a rich spectral structure that leads to rather good agreement with extant Lanczos results and offers a transparent picture of the underlying physics. It also leads naturally to two distinct regimes of spectral behavior, Δ0Z/D≫1 and ≪1 (with Z the quasiparticle weight), whose existence and essential characteristics are discussed and shown to be independent of 2PT itself. The self-energy ∑i(ω) is also examined beyond the confines of PT. It is argued that on frequency scales of order ω∼Δ0D, the self-energy in strong coupling is given precisely by the 2PT result, and we point out that the resultant poles in ∑i(ω) connect continuously to that characteristic of the atomic limit. This in turn offers a natural rationale for the known inability of the skeleton expansion to capture such behavior, and points to the intrinsic dangers of partial infinite-order summations that are based on PT in U. |
| first_indexed | 2024-03-06T20:15:29Z |
| format | Journal article |
| id | oxford-uuid:2bffacb3-ef44-400d-998a-567ab3c5adf0 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:15:29Z |
| publishDate | 2001 |
| record_format | dspace |
| spelling | oxford-uuid:2bffacb3-ef44-400d-998a-567ab3c5adf02022-03-26T12:34:20ZSpectral properties of a narrow-band Anderson modelJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2bffacb3-ef44-400d-998a-567ab3c5adf0EnglishSymplectic Elements at Oxford2001Schafer, SLogan, DWe consider single-particle spectra of a symmetric narrow-band Anderson impurity model, where the host bandwidth D is small compared to the hybridization strength Δ0. Simple second-order perturbation theory (2PT) in U is found to produce a rich spectral structure that leads to rather good agreement with extant Lanczos results and offers a transparent picture of the underlying physics. It also leads naturally to two distinct regimes of spectral behavior, Δ0Z/D≫1 and ≪1 (with Z the quasiparticle weight), whose existence and essential characteristics are discussed and shown to be independent of 2PT itself. The self-energy ∑i(ω) is also examined beyond the confines of PT. It is argued that on frequency scales of order ω∼Δ0D, the self-energy in strong coupling is given precisely by the 2PT result, and we point out that the resultant poles in ∑i(ω) connect continuously to that characteristic of the atomic limit. This in turn offers a natural rationale for the known inability of the skeleton expansion to capture such behavior, and points to the intrinsic dangers of partial infinite-order summations that are based on PT in U. |
| spellingShingle | Schafer, S Logan, D Spectral properties of a narrow-band Anderson model |
| title | Spectral properties of a narrow-band Anderson model |
| title_full | Spectral properties of a narrow-band Anderson model |
| title_fullStr | Spectral properties of a narrow-band Anderson model |
| title_full_unstemmed | Spectral properties of a narrow-band Anderson model |
| title_short | Spectral properties of a narrow-band Anderson model |
| title_sort | spectral properties of a narrow band anderson model |
| work_keys_str_mv | AT schafers spectralpropertiesofanarrowbandandersonmodel AT logand spectralpropertiesofanarrowbandandersonmodel |