Exact ordering of energy levels for one-dimensional interacting Fermi gases with $SU(n)$ symmetry

Abstract

Based on the exact solution of one-dimensional Fermi gas systems with $SU(n)$ symmetry in a hard wall, we demonstrate that we are able to sort the ordering of the lowest energy eigenvalues of states with all allowed permutation symmetries, which can be solely marked by certain quantum numbers in the Bethe ansatz equations. Our results give examples beyond the scope of the generalized Lieb-Mattis theorem, which can only compare the ordering of energy levels of states belonging to different symmetry classes if they are comparable according to the pouring principle. In the strongly interacting regime, we show that the ordering of energy levels can be determined by an effective spin-exchange model and extend our results to the non-uniform system trapped in the harmonic potential.

6 pages, 4 figures

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• Universal Tan relations for quantum gases in one dimension
• Strongly correlated one-dimensional Bose-Fermi quantum mixtures: symmetry and correlations
• Momentum distribution and contacts of one-dimensional spinless Fermi gases with an attractive p-wave interaction
• Symmetries and Correlations in Strongly Interacting One-dimensional Quantum Gases
• Local manipulation of quantum magnetism in 1D ultracold Fermi gases across narrow resonances
• Strongly Repulsive 1D Gases at Higher Branches: Spin-Charge Correlation and Coupled Spin-Chain Model
• Generation of spin currents by a temperature gradient in a two-terminal device