The spin-one Motzkin chain is gapped for any area weight $t<1$ (opens in new tab)

arXiv:2204.04517v2 Announce Type: replace-cross Abstract: We consider the spin-one Motzkin chain with area weight $t>0$. We resolve three questions from the literature about this model. We prove (i) existence of a uniform spectral gap for all $t1$ is robust and extends to hard boundary conditions, answering a question of Zhang--Klich \cite{zhang2017entropy}. These conclusions rest on an effective approximate description of the ground states of finite open Motzkin chains in terms of height-con...