标题： 原子链的合成视界与热化及其与量子霍尔系统的关系 显示英文标题

标题： Synthetic Horizons and Thermalization in an Atomic Chain and its Relation to Quantum Hall Systems

摘要： 我们研究了正弦模型，这是一种具有一维紧束缚哈密顿量的模型，其中跃迁幅度随位置呈正弦依赖性，并展示了电子波包表现出指数减速时人工视界的形成。有趣的是，利用该模型与Harper方程之间的精确变换（Harper方程描述了受到垂直磁场作用的方形晶格紧束缚模型的本征态），我们发现，在量子霍尔体系半满填充时，对于特定的磁通量值，类似的半经典视界可以出现。此外，通过对正弦模型的跃迁特性施加突然淬火，我们观察到具有Unruh温度的热态的出现。我们的数值计算表明这种温度表现出非普适的行为，这表明涉及的物理机制超出了简单的低能描述。 显示英文摘要

摘要： We investigate the sine model, a one-dimensional tight-binding Hamiltonian featuring hoppings with a sinusoidal dependence on position, and demonstrate the formation of synthetic horizons where electronic wave packets exhibit exponential slowdown. Interestingly, employing the exact transformation between this model and the Harper equation, which describes the eigenstates of a square lattice tight-binding model subjected to a perpendicular magnetic field, we find that analogous semi-classical horizons can emerge in a quantum Hall setup at half-filling for specific values of the magnetic flux. Furthermore, by applying sudden quenches to the sine model's hopping profile, we observe the emergence of thermal states characterized by an Unruh temperature. Our numerical calculations of this temperature reveal a non-universal behavior, suggesting the involvement of physical mechanisms beyond a simple low-energy description.