We present a class of Hamiltonians $H$ for which a sector of the Hilbert space invariant under a Lie group $G$, which is not a symmetry of $H$, possesses the essential properties of many-body scar states. These include the absence of thermalization and the “revivals” of special initial states in time evolution. A particular class of examples concerns interacting spin-1/2 fermions on a lattice consisting of $N$ sites (it includes deformations of the Fermi-Hubbard model as special cases), and we show that it contains two families of $N+1$ scar states. One of these families, which was found in recent literature, is comprised of the well-known $\eta$-pairing states. We find another family of scar states which is $U(N)$ invariant. Both families and most of the group-invariant scar states produced by our construction in general, give rise to the off-diagonal long range order which survives at high temperatures and is insensitive to the details of the dynamics. Such states could be used for reliable quantum information processing because the information is stored non-locally, and thus cannot be easily erased by local perturbations. In contrast, other scar states we find are product states which could be easily prepared experimentally. The dimension of scar subspace is directly controlled by the choice of group $G$ and can be made exponentially large.

中文翻译：

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多体疤痕作为希尔伯特空间的一组不变扇区

我们提出一类哈密顿主义者 $H$ 李群下希尔伯特空间不变的一个扇区 $G$，这不是对称的 $H$拥有多体疤痕状态的基本特性。这些包括时间过程中不存在热化作用和特殊初始状态的“恢复”。一类特殊的例子涉及相互作用自旋1/2费米子在由$ñ$ 站点（其中包括Fermi-Hubbard模型的变形作为特殊情况），我们表明它包含两个族 $ñ+\mathrm{1个}$疤痕状态。在最近的文献中发现了其中一个家族，其中包括著名的$\eta$配对状态。我们发现了另一个疤痕状态家族$ü（ñ）$不变的 通常，我们的构造产生的家族和大多数群体不变的疤痕状态都会产生对角线的远距离顺序，该顺序在高温下仍然存在，并且对动力学的细节不敏感。这样的状态可以用于可靠的量子信息处理，因为该信息是非本地存储的，因此不易被本地扰动擦除。相反，我们发现的其他疤痕状态是可以通过实验轻松制备的产品状态。疤痕空间的大小直接受组的选择控制$G$ 并可以成倍增大