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Exact ordering of energy levels for one-dimensional interacting Fermi gases with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mi>U</mml:mi></mml:mrow></mml:math> (N) symmetry
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 …