Lieb-Mattis ordering theorem of electronic energy levels in the thermodynamic limit

• URL: http://arxiv.org/abs/2505.17081v2
• Date: Tue, 03 Jun 2025 10:42:33 GMT
• Title: Lieb-Mattis ordering theorem of electronic energy levels in the thermodynamic limit
• Authors: Manuel Calixto, Alberto Mayorgas, Julio Guerrero,
• Abstract summary: Lieb-Mattis theorem orders the lowest-energy states of total spin $s$ of a system of $P$ interacting fermions.<n>We generalize these predictions to fermionic mixtures of $P$ particles with more than $N=2$ spinor components/species.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\lambda_c(h)$ of the exchange coupling constant $\lambda$, depending on $h$. This generalizes standard quantum phase transitions and their phase diagrams corresponding to the ground state belonging to the most symmetric sector $h_0$.

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