Pakrouski K, Pallegar P N, Popov F K, Klebanov I R
Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev Lett. 2020 Dec 4;125(23):230602. doi: 10.1103/PhysRevLett.125.230602.
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, comprises the well-known η-pairing states. We find another family of scar states that 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 nonlocally 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.
我们展示了一类哈密顿量H，对于其希尔伯特空间的一个在李群G下不变的扇区（G不是H的对称性），具有多体疤痕态的基本性质。这些性质包括不存在热化以及特殊初始态在时间演化中的“复苏”。一类特殊的例子涉及在由N个格点组成的晶格上相互作用的自旋 - 1/2费米子（它包括费米 - 哈伯德模型的变形作为特殊情况），并且我们表明它包含两个由N + 1个疤痕态组成的族。其中一个族，是近期文献中发现的，由著名的η配对态组成。我们发现了另一个U(N)不变的疤痕态族。一般来说，这两个族以及我们构造产生的大多数群不变疤痕态都会产生非对角长程有序，这种有序在高温下仍然存在并且对动力学细节不敏感。这样的态可用于可靠的量子信息处理，因为信息是非局域存储的，因此不容易被局部微扰擦除。相比之下，我们发现的其他疤痕态是乘积态，它们可以很容易地通过实验制备。疤痕子空间的维度直接由群G的选择控制，并且可以变得指数级大。
