Fermi liquid theory: a renormalization group point of view
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arXiv
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| Format: | Preprint |
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1996
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| _version_ | 1866913497143574528 |
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| author | Dupuis, N. |
| author_facet | Dupuis, N. |
| contents | We show how Fermi liquid theory results can be systematically recovered using a renormalization group (RG) approach. Considering a two-dimensional system with a circular Fermi surface, we derive RG equations at one-loop order for the two-particle vertex function $Γ$ in the limit of small momentum (${\bf Q}$) and energy ($Ω$) transfer and obtain the equation which determines the collective modes of a Fermi liquid. The density-density response function is also calculated. The Landau function (or, equivalently, the Landau parameters $F_l^s$ and $F_l^a$) is determined by the fixed point value of the $Ω$-limit of the two-particle vertex function (${Γ^Ω}^*$). We show how the results obtained at one-loop order can be extended to all orders in a loop expansion. Calculating the quasi-particle life-time and renormalization factor at two-loop order, we reproduce the results obtained from two-dimensional bosonization or Ward Identities. We discuss the zero-temperature limit of the RG equations and the difference between the Field Theory and the Kadanoff-Wilson formulations of the RG. We point out the importance of $n$-body ($n\geq 3$) interactions in the latter. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_cond_mat_9604189 |
| institution | arXiv |
| publishDate | 1996 |
| record_format | arxiv |
| spellingShingle | Fermi liquid theory: a renormalization group point of view Dupuis, N. Condensed Matter We show how Fermi liquid theory results can be systematically recovered using a renormalization group (RG) approach. Considering a two-dimensional system with a circular Fermi surface, we derive RG equations at one-loop order for the two-particle vertex function $Γ$ in the limit of small momentum (${\bf Q}$) and energy ($Ω$) transfer and obtain the equation which determines the collective modes of a Fermi liquid. The density-density response function is also calculated. The Landau function (or, equivalently, the Landau parameters $F_l^s$ and $F_l^a$) is determined by the fixed point value of the $Ω$-limit of the two-particle vertex function (${Γ^Ω}^*$). We show how the results obtained at one-loop order can be extended to all orders in a loop expansion. Calculating the quasi-particle life-time and renormalization factor at two-loop order, we reproduce the results obtained from two-dimensional bosonization or Ward Identities. We discuss the zero-temperature limit of the RG equations and the difference between the Field Theory and the Kadanoff-Wilson formulations of the RG. We point out the importance of $n$-body ($n\geq 3$) interactions in the latter. |
| title | Fermi liquid theory: a renormalization group point of view |
| topic | Condensed Matter |
| url | https://arxiv.org/abs/cond-mat/9604189 |