Lieb-Mattis ordering theorem of electronic energy levels in the thermodynamic limit
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866908814803992576 |
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| author | Calixto, Manuel Mayorgas, Alberto Guerrero, Julio |
| author_facet | Calixto, Manuel Mayorgas, Alberto Guerrero, Julio |
| contents | Lieb-Mattis theorem orders the lowest-energy states of total spin $s$ of a system of $P$ interacting fermions. We generalize these predictions to fermionic mixtures of $P$ particles with more than $N=2$ spinor components/species in the thermodynamic limit $P\to\infty$. The lowest-energy state inside each permutation symmetry sector $h$, arising in the $P$-fold tensor product decomposition, is well approximated by a U$(N)$ coherent (quasi-classical, variational) state, specially in the limit $P\to\infty$. In particular, the ground state of the system belongs the most symmetric (dominant Young tableau $h_0$) configuration. We exemplify our construction with the $N=3$ level Lipkin-Meshkov-Glick model, with a previous motivation on pairing correlations and U$(N)$-invariant quantum Hall ferromagnets. In the limit $P\to\infty$, each lowest-energy state within each permutation symmetry sector $h$ undergoes a quantum phase transition for a critical value $λ_c(h)$ of the exchange coupling constant $λ$, depending on $h$. This generalizes standard quantum phase transitions and their phase diagrams corresponding to the ground state belonging to the most symmetric sector $h_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17081 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lieb-Mattis ordering theorem of electronic energy levels in the thermodynamic limit Calixto, Manuel Mayorgas, Alberto Guerrero, Julio Strongly Correlated Electrons Mesoscale and Nanoscale Physics Mathematical Physics Quantum Physics Lieb-Mattis theorem orders the lowest-energy states of total spin $s$ of a system of $P$ interacting fermions. We generalize these predictions to fermionic mixtures of $P$ particles with more than $N=2$ spinor components/species in the thermodynamic limit $P\to\infty$. The lowest-energy state inside each permutation symmetry sector $h$, arising in the $P$-fold tensor product decomposition, is well approximated by a U$(N)$ coherent (quasi-classical, variational) state, specially in the limit $P\to\infty$. In particular, the ground state of the system belongs the most symmetric (dominant Young tableau $h_0$) configuration. We exemplify our construction with the $N=3$ level Lipkin-Meshkov-Glick model, with a previous motivation on pairing correlations and U$(N)$-invariant quantum Hall ferromagnets. In the limit $P\to\infty$, each lowest-energy state within each permutation symmetry sector $h$ undergoes a quantum phase transition for a critical value $λ_c(h)$ of the exchange coupling constant $λ$, depending on $h$. This generalizes standard quantum phase transitions and their phase diagrams corresponding to the ground state belonging to the most symmetric sector $h_0$. |
| title | Lieb-Mattis ordering theorem of electronic energy levels in the thermodynamic limit |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2505.17081 |