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Exact ordering of energy levels for one-dimensional interacting Fermi gases with $SU(n)$ symmetry | | Lei Pan
; Yanxia Liu
; Haiping Hu
; Yunbo Zhang
; Shu Chen
; | | Date: |
10 Feb 2017 | | Abstract: | Based on the exact solution of one-dimensional Fermi gas systems with $SU(n)$
symmetry, we demonstrate that it is possible to sort the ordering 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 go beyond 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 rule can be determined by an
effective spin-exchange model and extend our results to the non-uniform system
trapped in the harmonic potential. Our results provide a rule for ordering the
high-spin $SU(n)$ symmetric systems. | | Source: | arXiv, 1702.3263 | | Services: | Forum | Review | PDF | Favorites | |
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