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

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 $h_0$.

arXiv comment14 pages, 3 figures, 2 gif as ancillary files

References in corpus (23)

• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Moire bands in twisted double-layer graphene
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Ultracold fermions and the SU(N) Hubbard model
• SU(N) gauge theories at large N
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• Excited state quantum phase transitions in many-body systems
• One-dimensional mixtures of several ultracold atoms: a review
• SU(N) Quantum Hall Skyrmions
• Moments of generalized Husimi distributions and complexity of many-body quantum states
• Bilayer Quantum Hall Systems at Filling Factor ν=2: An Exact Diagonalisation Study
• Exact density profiles and symmetry classification for strongly interacting multi-component Fermi gases in tight waveguides
• Continuous unitary transformations in two-level boson systems
• SU(N) Fermions in a One-Dimensional Harmonic Trap
• Polychromatic phase diagram for $n$-level atoms interacting with $\ell$ modes of electromagnetic field
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Ground-State Structure in $\nu =2$ Bilayer Quantum Hall Systems
• Role of mixed permutation symmetry sectors in the thermodynamic limit of critical three-level Lipkin-Meshkov-Glick atom models
• Variational Study of $\lambda$- and $N$-Atomic Configurations Interacting with an Electromagnetic Field of $2$ Modes
• Hilbert space and ground state structure of bilayer quantum Hall systems at $\nu =2/\lambda$
• Hilbert space structure of the low energy sector of U(N) quantum Hall ferromagnets and their classical limit
• Capturing magic angles in twisted bilayer graphene from information theory markers