论文标题
无挫败感的完全包装循环模型
The frustration-free fully packed loop model
论文作者
论文摘要
我们考虑在方格上使用无挫败的投影仪哈密顿量和戒指交换相互作用的量子完全包装的循环模型。添加边界哈密顿量以偏爱域壁边界条件，并将基态特性与组合型和六个vertex模型文献联系起来。我们讨论了边界项如何将希尔伯特空间骨折到克里洛夫子空间中，并证明哈密顿量在每个子空间内都是ergodic的，导致一系列能量等定位的精确特征态在频谱的下端。其中，我们系统地将有限纠缠的本征和产品本征态分类。使用递归关系来列举半平面构型，我们从数值上计算基态的确切纠缠熵，确认区域定律缩放。最后，该光谱在热力学极限中表现出无间隙，并通过为基态叠加增加扭曲而构建的试验状态。
We consider a quantum fully packed loop model on the square lattice with a frustration-free projector 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 a recursion relation for enumerating half-plane configurations, we compute numerically the exact entanglement entropy of the ground state, confirming area law scaling. Finally, the spectrum is shown to be gapless in the thermodynamic limit with a trial state constructed by adding a twist to the ground state superposition.
