Group theoretic approach to many-body scar states in fermionic lattice models
Group theoretic approach to many-body scar states in fermionic lattice models
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DOI：
10.1103/physrevresearch.3.043156
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发表时间：
2021-06
影响因子：
4.2
通讯作者：
K. Pakrouski;P. N. Pallegar;F. Popov;I. Klebanov
中科院分区：
文献类型：
--
作者：
K. Pakrouski;P. N. Pallegar;F. Popov;I. Klebanov
已经证明[arXiv：2007.00845]，对于任何自旋为1/2的费米子哈密顿量形式为$H_0+OT$，其中$T$是适当李群的生成元，三个高度对称态族是多体伤疤。这些家庭之一，包括著名的$\eta$配对状态。除了具有通常的疤痕性质外，这些状态族对电磁噪声不敏感，并且具有存储和处理量子信息的优势。在本文中，我们表明，一些著名的耦合项，如哈伯德和海森堡相互作用，以及包含它们的哈密顿量，是所需的形式，并支持这些国家的疤痕没有微调。给出了一些最常用的模型（包括拓扑模型）的显式H_0 +OT分解。为了方便可能的实验实现，我们讨论了这些模型的低能量子空间仅由疤痕组成的条件。此外，我们写下了所有的发电机$T$，可以用来作为构建模块，设计新的模型与疤痕，最有趣的是，包括自旋轨道耦合跳跃和超导配对条款。我们将这个框架扩展到非厄米特开放系统，并证明了对它们来说，疤痕子空间继续经历相干时间演化，并表现出“复兴”。一个完整的数值研究的扩展2D $tJU$模型明确说明了新的属性不变的疤痕，并支持我们的研究结果。
It has been shown [arXiv:2007.00845] that three families of highly symmetric states are many-body scars for any spin-1/2 fermionic Hamiltonian of the form $H_0+OT$, where $T$ is a generator of an appropriate Lie group. One of these families consists of the well-known $\eta$-pairing states. In addition to having the usual properties of scars, these families of states are insensitive to electromagnetic noise and have advantages for storing and processing quantum information. In this paper we show that a number of well-known coupling terms, such as the Hubbard and the Heisenberg interactions, and the Hamiltonians containing them, are of the required form and support these states as scars without fine-tuning. The explicit $H_0+OT$ decomposition for a number of most commonly used models, including topological ones, is provided. To facilitate possible experimental implementations, we discuss the conditions for the low-energy subspace of these models to be comprised solely of scars. Further, we write down all the generators $T$ that can be used as building blocks for designing new models with scars, most interestingly including the spin-orbit coupled hopping and superconducting pairing terms. We expand this framework to the non-Hermitian open systems and demonstrate that for them the scar subspace continues to undergo coherent time evolution and exhibit the"revivals". A full numerical study of an extended 2D $tJU$ model explicitly illustrates the novel properties of the invariant scars and supports our findings.