Area law violations and quantum phase transitions in modified Motzkin walk spin chains
Area law violations and quantum phase transitions in modified Motzkin walk spin chains
复制标题
改进的莫茨金步行自旋链中的区域违法和量子相变
DOI：
10.1088/1742-5468/aa9dcb
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Pramod Padmanabhan
中科院分区：
文献类型：
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作者：
Fumihiko Sugino;Pramod Padmanabhan
最近，基于莫茨金游走及其变体的一维无挫败量子系统研究了平方根形式的纠缠熵的面积定律违反情况。在这里，我们考虑 Motzkin 游走，该游走的每一步都有不同的希尔伯特空间，由对称逆半群的元素跨越，每一步的方向由其代数结构控制。这种变化改变了莫茨金步行中允许的路径数量，并引入了对边界扰动敏感的基态简并。我们研究基于三个对称逆半群 S13、S23 和 S12 的无挫败自旋链。基于S13和S23的系统提供了一维量子相变的例子，前者表现出面积定律和对数违反面积定律之间的转变，后者提供了系统尺寸从对数缩放到平方根缩放的转变示例，模仿彩色S13系统。 S12 的系统要简单得多，并且会产生继续遵守区域法的状态。
Area law violations for entanglement entropy in the form of a square root have recently been studied for one-dimensional frustration-free quantum systems based on the Motzkin walks and their variations. Here we consider a Motzkin walk with a different Hilbert space on each step of the walk spanned by the elements of a symmetric inverse semigroup with the direction of each step governed by its algebraic structure. This change alters the number of paths allowed in the Motzkin walk and introduces a ground state degeneracy that is sensitive to boundary perturbations. We study the frustration-free spin chains based on three symmetric inverse semigroups, S13, S23 and S12. The system based on S13 and S23 provides examples of quantum phase transitions in one dimension, with the former exhibiting a transition between the area law and a logarithmic violation of the area law and the latter providing an example of transition from logarithmic scaling to a square root scaling in the system size, mimicking a colored S13 system. The system with S12 is much simpler and produces states that continue to obey the area law.
无间隙量子自旋链：多重动力学和共形波函数
DOI：
10.1088/1751-8121/aa8dbc
发表时间：
2017
期刊：
Journal of Physics A: Mathematical and Theoretical
影响因子：
--
作者：
Chen, Xiao;Fradkin, Eduardo;Witczak-Krempa, William
通讯作者：
Witczak-Krempa, William