Unfrustration Condition and Degeneracy of Qudits on Trees    [PDF]

Matthew Coudron, Ramis Movassagh
We generalize the previous results of [1] by proving unfrustration condition and degeneracy of the ground states of qudits ($d-$dimensional spins) on a $k-$child tree with generic local interactions. We find that the dimension of the ground space grows doubly exponentially in the region where $rk\leq\frac{d^2}{4}$ for $k>1$. Further, we extend the results in [1] by proving that there are no zero energy ground states when $r>\frac{d^2}{4}$ for $k=1$ implying that the effective Hamiltonian is invertible.
View original: http://arxiv.org/abs/1209.4395