Unfrustration Condition and Degeneracy of Qudits on Trees

Matthew Coudron; Ramis Movassagh

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arXiv · 1209.4395

Unfrustration Condition and Degeneracy of Qudits on Trees

Matthew Coudron·Ramis Movassagh

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Abstract

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<=(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>(d^2)/4 for k=1 implying that the effective Hamiltonian is invertible.

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Matthew Coudron, Ramis Movassagh. 2012-09-20. Unfrustration Condition and Degeneracy of Qudits on Trees. https://arxiv.org/abs/1209.4395

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