2025/05/20 by Calixto, Manuel, Mayorgas, Alberto, Guerrero, Julio
#FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2505.17081
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→∞. 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→∞. In particular, the ground state of the system belongs the most symmetric (dominant Young tableau h0) 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→∞, each lowest-energy state within each permutation symmetry sector h undergoes a quantum phase transition for a critical value λc(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 h0.