论文标题
来自量子六个和19位vertex型号的耦合的弗雷德金和motzkin链
Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models
论文作者
论文摘要
我们通过建立具有相关相互作用的六个和十九个vertex模型来概括违反弗雷德金和motzkin自旋链模型的区域。哈密顿量无挫败感，其投影仪在高度配置的子空间内产生千古动态，这是非负面的。基态是经典的双色顶点配置的体积和颜色加权的叠加，在边界上的散装高度和零高度为零高。随着$ q $ - 定义参数的调整，子系统之间的纠缠熵具有相变，在存在外部田间的情况下，该参数在颜色的自由度上表现出强大。基态在区域和体积法纠缠阶段之间进行量子相变，其关键点，纠缠熵尺度作为函数$ l \ log l $ l \ log l $的线性系统大小$ l $。 $ l \ log l $和$ l^2 $之间的中级功率法量表可以通过不均匀的变形参数来实现，该参数在热力学限制中以不同的速率接近1。对于$ q> 1 $阶段，我们构建了一个变异波函数，该函数在光谱间隙上建立上限为$ q^{ - l^3/8} $。
We generalize the area-law violating models of Fredkin and Motzkin spin chains into two dimensions by building quantum six- and nineteen-vertex models with correlated interactions. The Hamiltonian is frustration free, and its projectors generate ergodic dynamics within the subspace of height configuration that are non negative. The ground state is a volume- and color-weighted superposition of classical bi-color vertex configurations with non-negative heights in the bulk and zero height on the boundary. The entanglement entropy between subsystems has a phase transition as the $q$-deformation parameter is tuned, which is shown to be robust in the presence of an external field acting on the color degree of freedom. The ground state undergoes a quantum phase transition between area- and volume-law entanglement phases with a critical point where entanglement entropy scales as a function $L\log L$ of the linear system size $L$. Intermediate power law scalings between $L\log L$ and $L^2$ can be achieved with an inhomogeneous deformation parameter that approaches 1 at different rates in the thermodynamic limit. For the $q>1$ phase, we construct a variational wave function that establishes an upper bound on the spectral gap that scales as $q^{-L^3/8}$.
