Momentum Distribution of a Fermi Gas in the Random Phase Approximation
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915180602982400 |
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| author | Benedikter, Niels Lill, Sascha |
| author_facet | Benedikter, Niels Lill, Sascha |
| contents | We consider a system of interacting fermions on the three-dimensional torus in a mean-field scaling limit. Our objective is computing the occupation number of the Fourier modes in a trial state obtained through the random phase approximation (in its collective bosonization formulation) for the ground state. We prove that the trial state's momentum distribution has a jump discontinuity, i.e., a well-defined Fermi surface. Moreover the Fermi momentum does not depend on the interaction potential (it is universal). Our result shows that the random phase approximation in the mean-field scaling limit is in principle sufficiently precise to identify a non-trivial Fermi liquid phase. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_02706 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Momentum Distribution of a Fermi Gas in the Random Phase Approximation Benedikter, Niels Lill, Sascha Mathematical Physics Quantum Gases Strongly Correlated Electrons 81V70, 82B10, 81Q10, 35P05 We consider a system of interacting fermions on the three-dimensional torus in a mean-field scaling limit. Our objective is computing the occupation number of the Fourier modes in a trial state obtained through the random phase approximation (in its collective bosonization formulation) for the ground state. We prove that the trial state's momentum distribution has a jump discontinuity, i.e., a well-defined Fermi surface. Moreover the Fermi momentum does not depend on the interaction potential (it is universal). Our result shows that the random phase approximation in the mean-field scaling limit is in principle sufficiently precise to identify a non-trivial Fermi liquid phase. |
| title | Momentum Distribution of a Fermi Gas in the Random Phase Approximation |
| topic | Mathematical Physics Quantum Gases Strongly Correlated Electrons 81V70, 82B10, 81Q10, 35P05 |
| url | https://arxiv.org/abs/2310.02706 |