Perturbative description of high-$T_c$ superconductivity in the Hubbard model via unitary transformation and classical spins
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909137723457536 |
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| author | Alpin, Kirill |
| author_facet | Alpin, Kirill |
| contents | A unitary transformation is applied to the Hubbard model, which maps the Hubbard interaction to a single particle term. The resulting Hamiltonian consists of unconstrained fermions, which is then mapped to a Hamiltonian of spinless fermions coupled to pseudospins. The fermions are integrated out using second order perturbation theory in $1/U$, resulting in an effective spin Hamiltonian. An order parameter is identified, stabilizing d-wave superconductivity. The groundstate energy of classical spin configurations is minimized at a finite value of this order parameter after a critical chemical potential, resulting in d-wave superconductivity at non-zero doping. This suggests, that the onset of high-$T_c$ superconductivity is governed by the groundstate of a classical spin system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09765 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Perturbative description of high-$T_c$ superconductivity in the Hubbard model via unitary transformation and classical spins Alpin, Kirill Strongly Correlated Electrons Superconductivity A unitary transformation is applied to the Hubbard model, which maps the Hubbard interaction to a single particle term. The resulting Hamiltonian consists of unconstrained fermions, which is then mapped to a Hamiltonian of spinless fermions coupled to pseudospins. The fermions are integrated out using second order perturbation theory in $1/U$, resulting in an effective spin Hamiltonian. An order parameter is identified, stabilizing d-wave superconductivity. The groundstate energy of classical spin configurations is minimized at a finite value of this order parameter after a critical chemical potential, resulting in d-wave superconductivity at non-zero doping. This suggests, that the onset of high-$T_c$ superconductivity is governed by the groundstate of a classical spin system. |
| title | Perturbative description of high-$T_c$ superconductivity in the Hubbard model via unitary transformation and classical spins |
| topic | Strongly Correlated Electrons Superconductivity |
| url | https://arxiv.org/abs/2403.09765 |