We study in detail the properties of the quantum East model, an interacting quantum spin chain inspired by simple kinetically constrained models of classical glasses. Through a combination of analytics, exact diagonalization, and tensor-network methods, we show the existence of a transition, from a fast to a slow thermalization regime, which manifests itself throughout the spectrum. On the slow side, by exploiting the localization of the ground state and the form of the Hamiltonian, we explicitly construct a large (exponential in size) number of nonthermal states that become exact finite-energy-density eigenstates in the large size limit, as expected for a true phase transition. A “superspin” generalization allows us to find a further large class of area-law states proved to display very slow relaxation. These states retain memory of their initial conditions for extremely long times. Our numerical analysis reveals that the localization properties are not limited to the ground state and that many eigenstates have large overlap with product states and can be approximated well by matrix product states at arbitrary energy densities. The mechanism that induces localization to the ground state, and hence the nonthermal behavior of the system, can be extended to a wide range of models including a number of simple spin chains. We discuss implications of our results for slow thermalization and nonergodicity more generally in disorder-free systems with constraints, and we give numerical evidence that these results may be extended to two-dimensional systems.

中文翻译：

---

量子东模型：局部化，非热本征态和慢动力学

我们详细研究了量子East模型的性质，该模型是由经典眼镜的简单动力学约束模型所启发的相互作用的量子自旋链。通过分析，精确的对角化和张量网络方法的组合，我们显示了从快速到慢速热化过程的过渡存在，这种过渡在整个光谱中都表现出来。另一方面，通过利用基态的局部化和哈密顿量的形式，我们显式地构造了大量（尺寸呈指数形式）的非热态，这些非热态在大尺寸范围内成为精确的有限能量密度本征态，如下期望实现真正的相变。“超自旋”泛化使我们能够找到另一类更大的面积律状态，这些状态被证明显示出非常缓慢的弛豫。这些状态会在很长一段时间内保留其初始状态的记忆。我们的数值分析表明，定位特性不限于基态，许多本征态与乘积态有很大的重叠，并且可以通过任意能量密度的矩阵乘积态很好地近似。可以将诱导局部化为基态的机制以及系统的非热行为扩展到包括许多简单自旋链在内的各种模型。我们讨论了在无约束的无障碍系统中，我们的结果对于缓慢的热化和非遍历性的影响，并且给出了数字证据，这些结果可能会扩展到二维系统。我们的数值分析表明，定位特性不限于基态，许多本征态与乘积态有很大的重叠，并且可以通过任意能量密度的矩阵乘积态很好地近似。可以将诱导局部化为基态的机制以及系统的非热行为扩展到包括许多简单自旋链在内的各种模型。我们讨论了在无约束的无障碍系统中，我们的结果对于缓慢的热化和非遍历性的影响，并且给出了数字证据，这些结果可能会扩展到二维系统。我们的数值分析表明，定位特性不限于基态，许多本征态与乘积态有很大的重叠，并且可以通过任意能量密度的矩阵乘积态很好地近似。可以将诱导局部化为基态的机制以及系统的非热行为扩展到包括许多简单自旋链在内的各种模型。我们讨论了在无约束的无障碍系统中，我们的结果对于缓慢的热化和非遍历性的影响，并且给出了数字证据，这些结果可能会扩展到二维系统。