论文标题
受保护的零模式及以后的疤痕（1）$量子链接和量子二聚体模型
Scars from protected zero modes and beyond in $U(1)$ quantum link and quantum dimer models
论文作者
论文摘要
我们在$ U（1）$ u（1）$量子链路和矩形晶格上存在异常的高能量特征状态或多体疤痕。特别是，我们考虑范式rokhsar-kivelson hamiltonian $ h = \ mathcal {o} _ {\ mathrm {kin}}} +λ\ mathcal {O} （$ \ mathcal {o} _ {\ mathrm {kin}} $）被定义为在计算基础上是对角线（偏高）的基本plaquettes上的术语之和。这两种相互作用的模型都具有指数级的中频零模式，该模式在$λ= 0 $的系统大小上，受索引定理保护，以防止在此耦合时与非零模式混合。我们将不同类型的疤痕分类为$ |λ| \ Lesssim \ Mathcal {O}（1）$均以零和有限绕组数字部门的补充，并显着概括了我们以前的工作[Banerjee and Sen，Phys。莱特牧师。 126，220601（2021）]。有限的$λ$的疤痕显示出丰富的种类，这些疤痕仅来自$ \ Mathcal {o} _ {\ Mathrm {kin}} $的零模式，这些模式均包含零和零零模式的$ \ \ \ nthcal {o} $ {o} $ { $ \ Mathcal {O} _ {\ Mathrm {kin}} $的非零模式。我们为矩形晶格上的量子二聚体模型提供了某些“乐高疤痕”的分析表达式，其中一个线性尺寸可以任意大，其中构建块（乐高）由出现的单线和其他更复杂的纠缠结构组成。
We demonstrate the presence of anomalous high-energy eigenstates, or many-body scars, in $U(1)$ quantum link and quantum dimer models on square and rectangular lattices. In particular, we consider the paradigmatic Rokhsar-Kivelson Hamiltonian $H=\mathcal{O}_{\mathrm{kin}} + λ\mathcal{O}_{\mathrm{pot}}$ where $\mathcal{O}_{\mathrm{pot}}$ ($\mathcal{O}_{\mathrm{kin}}$) is defined as a sum of terms on elementary plaquettes that are diagonal (off-diagonal) in the computational basis. Both these interacting models possess an exponentially large number of mid-spectrum zero modes in system size at $λ=0$ that are protected by an index theorem preventing any mixing with the nonzero modes at this coupling. We classify different types of scars for $|λ| \lesssim \mathcal{O}(1)$ both at zero and finite winding number sectors complementing and significantly generalizing our previous work [Banerjee and Sen, Phys. Rev. Lett. 126, 220601 (2021)]. The scars at finite $λ$ show a rich variety with those that are composed solely from the zero modes of $\mathcal{O}_{\mathrm{kin}}$, those that contain an admixture of both the zero and the nonzero modes of $\mathcal{O}_{\mathrm{kin}}$, and finally those composed solely from the nonzero modes of $\mathcal{O}_{\mathrm{kin}}$. We give analytic expressions for certain "lego scars" for the quantum dimer model on rectangular lattices where one of the linear dimensions can be made arbitrarily large, with the building blocks (legos) being composed of emergent singlets and other more complicated entangled structures.
