Hartree-Fock with Nambu spinors, and d-wave condensation in the 2D Hubbard model
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929479807401984 |
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| author | Matsuyama, Kazue Greensite, Jeff |
| author_facet | Matsuyama, Kazue Greensite, Jeff |
| contents | The usual Hartree-Fock approximation to the Hubbard model is based on eigenstates of the electron number operator. But this formulation is not unique. A different (and inequivalent) version, formulated in terms of Nambu two-component spinors, is based on eigenstates of the difference between the numbers of spin up and spin down electrons, with electron density dependent on parameters $U,t,t'$ and chemical potential $μ$. The advantage of this formulation is that electron pairing condensates can be directly computed. We show that in the ground states away from half-filling, obtained in this "Nambu" Hartree-Fock approximation, a discrete rotation symmetry is spontaneously broken, and the condensates exhibit the expected d-wave form in momentum space. We also show that the Mott insulator electron configuration is obtained in this formulation at large $U/t$ and half-filling, and roughly locate the boundary, in the hole doping$-$$U/t$ plane, between a region of local antiferromagnetism and stripe/domain formation, and the region of d-wave condensation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_06674 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hartree-Fock with Nambu spinors, and d-wave condensation in the 2D Hubbard model Matsuyama, Kazue Greensite, Jeff Strongly Correlated Electrons Superconductivity High Energy Physics - Lattice The usual Hartree-Fock approximation to the Hubbard model is based on eigenstates of the electron number operator. But this formulation is not unique. A different (and inequivalent) version, formulated in terms of Nambu two-component spinors, is based on eigenstates of the difference between the numbers of spin up and spin down electrons, with electron density dependent on parameters $U,t,t'$ and chemical potential $μ$. The advantage of this formulation is that electron pairing condensates can be directly computed. We show that in the ground states away from half-filling, obtained in this "Nambu" Hartree-Fock approximation, a discrete rotation symmetry is spontaneously broken, and the condensates exhibit the expected d-wave form in momentum space. We also show that the Mott insulator electron configuration is obtained in this formulation at large $U/t$ and half-filling, and roughly locate the boundary, in the hole doping$-$$U/t$ plane, between a region of local antiferromagnetism and stripe/domain formation, and the region of d-wave condensation. |
| title | Hartree-Fock with Nambu spinors, and d-wave condensation in the 2D Hubbard model |
| topic | Strongly Correlated Electrons Superconductivity High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2210.06674 |