论文标题
旋转的Motzkin连锁链被限制在任何区域重量$ t <1 $
The spin-one Motzkin chain is gapped for any area weight $t<1$
论文作者
论文摘要
我们证明了张，艾哈迈达因和克里奇的猜想，即旋转$ 1 $ motzkin的链条均适用于任何面积重量$ t <1 $。对于Motzkin Hamiltonian属于Haldane阶段而言，必须存在有限的光谱差距，这在最近的Barbiero，Dell'anna，Trombettoni和Korepin的工作中被认为是这种情况。我们的证明取决于地面空间的组合结构以及有限大小的标准的分析验证。
We prove a conjecture by Zhang, Ahmadain, and Klich that the spin-$1$ Motzkin chain is gapped for any area weight $t<1$. Existence of a finite spectral gap is necessary for the Motzkin Hamiltonian to belong to the Haldane phase, which has been argued to potentially be the case in recent work of Barbiero, Dell'Anna, Trombettoni, and Korepin. Our proof rests on the combinatorial structure of the ground space and the analytical verification of a finite-size criterion.
