Exact eigenstates of extended <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>SU</mml:mi><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:math> Hubbard models: Generalization of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>η</mml:mi></mml:math>-pairing states with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>-particle off-diagonal long-range order
Hironobu Yoshida, Hosho Katsura
Abstract
We consider $N$-particle generalizations of $\ensuremath{\eta}$-pairing states in a chain of $N$-component fermions and show that these states are exact (high-energy) eigenstates of an extended $\mathrm{SU}(N)$ Hubbard model. We compute the singlet correlation function of the states and find that its behavior is qualitatively different for even and odd $N$. When $N$ is even, these states exhibit off-diagonal long-range order in $N$-particle reduced density matrix. On the other hand, when $N$ is odd, the correlations decay exponentially with distance in the bulk, but end-to-end correlations do not vanish in the thermodynamic limit. Finally, we prove that these states are the unique ground states of suitably tailored Hamiltonians.