论文标题
AKLT和其他型号中疤痕状态的精确塔的统一结构
Unified structure for exact towers of scar states in the AKLT and other models
论文作者
论文摘要
量子多体疤痕状态是多体状态，在不遵守本征态热假说的不可融合模型中具有有限的能量密度。最近的作品揭示了疤痕状态的“塔”，这些状态的“塔”是完全已知的，并且在能量方面均具有相同的间隔，特别是在AKLT模型中，Spin-1 XY模型和一个旋转1/2模型，可保存域壁数量。我们通过评估汉密尔顿和梯子操作员的换向器来提供一个共同的框架，以了解和证明这些系统中已知的疤痕确切塔。特别是，我们通过研究两个站点旋转投影仪，提供了整数旋转1D AKLT模型中疤痕塔的简单证明。通过这张照片，我们推断出一个与AKLT模型共享疤痕塔的汉密尔顿家族，还为AKLT和XY模型疤痕找到了普通的Hamiltonians。我们还通过连续应用非本地梯子操作员在Spin-1/2模型中介绍了以“金字塔”结构组织的确切状态的新塔。
Quantum many-body scar states are many-body states with finite energy density in non-integrable models that do not obey the eigenstate thermalization hypothesis. Recent works have revealed "towers" of scar states that are exactly known and are equally spaced in energy, specifically in the AKLT model, the spin-1 XY model, and a spin-1/2 model that conserves number of domain walls. We provide a common framework to understand and prove known exact towers of scars in these systems, by evaluating the commutator of the Hamiltonian and a ladder operator. In particular we provide a simple proof of the scar towers in the integer-spin 1d AKLT models by studying two-site spin projectors. Through this picture we deduce a family of Hamiltonians that share the scar tower with the AKLT model, and also find common parent Hamiltonians for the AKLT and XY model scars. We also introduce new towers of exact states, organized in a "pyramid" structure, in the spin-1/2 model through successive application of a non-local ladder operator.
