Lowest energy states of an $O(N)$ fermionic chain

Abstract

A quite general finite-size chain of fermions with $N$ internal degrees of freedom (flavors) and $O(N)$ symmetry is considered. In the case of the free boundary condition, we prove that the ground state in the invariant sector having exactly $m$ flavors with an odd particle number is represented by a single rank-$m$ antisymmetric multiplet. For the even-length chains, its particle-hole quantum number (if it's a good one) is given by the parity of the $m$. For the odd-length chains, the particle-hole symmetry leads to the twofold degeneracy among the conjugate multiplets. Similar statements are proven for the $O(N)$ mixed-spin chains in antisymmetric representations. The results are extended to the long-range interacting fermions and (partially) to the translation invariant chains.

Expanded version accepted in Phys. Rev. B. The spectrum of two-site chains is calculated, and the spin chains are discussed in more detail. Formulas and two figures are added, misprints corrected. 20 pages

References in corpus (5)

• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Ultracold fermions and the SU(N) Hubbard model
• Strongly interacting Majorana fermions
• The ordering of energy levels for SU(n) symmetric antiferromagnetic chains
• Ordering of Energy Levels for Extended SU(N) Hubbard Chain