论文标题
量子lizenge瓷砖和纠缠相变
Quantum lozenge tiling and entanglement phase transition
论文作者
论文摘要
虽然违反区域法的体积违反了几个量子自旋链，但在较高维度上纠缠不止一个方向的相应基态的构建一直是一个悬而未决的问题。在这里，我们在最大程度地违反了该地区法律的情况下构建了一个无挫败的哈密顿官。我们这样做是通过建立具有颜色自由度的随机表面量子模型，该模型可以看作是彩色戴克路径的集合。哈密顿量可能被视为弗雷德金自旋链的2D概括。它关联了所有有色的随机表面构型，受到迪利奇边界条件和硬壁约束的影响，因此基态是所有这些经典状态和非脱位的叠加。随着变形参数的调整，子系统之间的纠缠熵会经历量子相变。区域和体积范围阶段类似于一维模型，而临界点尺度则以系统$ l $为$ l \ log l $的线性大小。此外，人们可以推测，具有纠缠相转换的类似模型可以在更高的维度建造，而在关键点上，违反区域的法律违规。
While volume violation of area law has been exhibited in several quantum spin chains, the construction of a corresponding ground state in higher dimensions, entangled in more than one direction, 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. It relates all the colored random surface configurations subject to a Dirichlet boundary condition and hard wall constraint from below to one another, and the ground state is therefore a superposition of all such classical states and non-degenerate. Its entanglement entropy between subsystems undergoes a quantum 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 $L\log L$. Further it is conjectured that similar models with entanglement phase transitions can be built in higher dimensions with even softer area law violations at the critical point.
