Hilbert space fragmentation in a frustration-free fully packed loop model
Hilbert space fragmentation in a frustration-free fully packed loop model
复制标题
无挫折全填充循环模型中的希尔伯特空间碎片
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Henrik Røising
中科院分区：
文献类型：
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作者：
Zhao Zhang;Henrik Røising
本文考虑了正方晶格上的量子完全填充圈模型，该模型具有无阻挫的投影哈密顿量和作用于格元上的环交换相互作用。添加了边界汉密尔顿算子以支持域壁边界条件并将基态性质与组合数学和六顶点模型文献联系起来。我们讨论了边界项如何将Hilbert空间分裂成Krylov子空间，并证明了每个子空间内的哈密顿量是遍历的，从而导致了一系列能量等距的精确本征态在低端的频谱。其中，我们系统地分类了有限纠缠本征态和乘积本征态。使用一个精确的递归关系和枚举的半平面完全包装的回路配置与不同的边界配置的一侧，我们进行了一个数值精确的晶格计算的基态二分纠缠熵，产生面积律标度。最后，光谱示出是无缝的热力学极限与审判波函数构造通过添加扭曲的基态叠加。
We consider a quantum fully packed loop model on the square lattice with a frustration-free pro-jector Hamiltonian and ring-exchange interactions acting on plaquettes. A boundary Hamiltonian is added to favour domain-wall boundary conditions and link ground state properties to the combinatorics and six-vertex model literature. We discuss how the boundary term fractures the Hilbert space into Krylov subspaces, and we prove that the Hamiltonian is ergodic within each subspace, leading to a series of energy-equidistant exact eigenstates in the lower end of the spectrum. Among them we systematically classify both finitely entangled eigenstates and product eigenstates. Using an exact recursion relation and the enumeration of half-plane fully packed loop configurations with varying boundary configurations on one side, we perform a numerically exact lattice calculation of the ground state bipartite entanglement entropy, yielding area law scaling. Finally, the spectrum is shown to be gapless in the thermodynamic limit with a trial wave function constructed by adding a twist to the ground state superposition.