Quantum colored lozenge tiling and entanglement phase transition
Quantum colored lozenge tiling and entanglement phase transition
复制标题
量子彩色菱形平铺和纠缠相变
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
I. Klich
中科院分区：
文献类型：
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作者：
Zhao Zhang;I. Klich
虽然在几个量子自旋链中已经表现出体积违反面积定律，但在更高维度中构建具有各向同性项的相应模型一直是一个悬而未决的问题。在这里，我们构建了一个2D的挫折免费哈密顿与最大违反面积定律。我们这样做是通过建立一个量子模型的随机表面的颜色自由度，可以被视为一个集合的彩色戴克路径。哈密顿量可以被看作是Fredkin自旋链的二维推广。它的行动被证明是遍历的零固定的Dirichlet边界条件和正的高度函数在体的希尔伯特子空间内，并表现出非退化的基态。随着形变参数的改变，子系统间的纠缠熵呈现出纠缠相变。面积法和体积法相类似于一维模型，而临界点的尺度与系统的线性尺寸L$为Llog L$。类似的模型可以建立在更高的维度上，在临界点处具有更软的面积定律违反。
While volume violation of area law has been exhibited in several quantum spin chains, the construction of a corresponding model in higher dimensions, with isotropic terms, has been an open problem. Here we construct a 2D frustration-free Hamiltonian with maximal violation of the area law. We do so by building a quantum model of random surfaces with color degree of freedom that can be viewed as a collection of colored Dyck paths. The Hamiltonian may be viewed as a 2D generalization of the Fredkin spin chain. Its action is shown to be ergodic within the Hilbert subspace of zero fixed Dirichlet boundary condition and positive height function in the bulk and exhibits a non-degenerate ground state. Its entanglement entropy between subsystems exhibits an entanglement phase transition as the deformation parameter is tuned. The area- and volume-law phases are similar to the one-dimensional model, while the critical point scales with the linear size of the system $L$ as $Llog L$. Similar models can be built in higher dimensions with even softer area law violations at the critical point.