论文标题
热力学极限中的绝热定理：具有均匀间隙的系统
Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap
论文作者
论文摘要
我们表明，关于相互作用的绝热理论的最新结果在有限晶格上差异多体系统在热力学极限中仍然有效。更确切地说，我们证明了自动形态组的广义超绝热定理，该定理描述了可观察到的准本地代数上的无限体积动力学。关键的假设是存在一系列有限体积哈密顿量的序列，该序列在热力学极限中产生相同的无限体积动力学。我们的绝热定理也适用于缩小光谱差距的某些凹陷状态的某些扰动（因此，它也是一种充气定理的共鸣定理，并且从这种意义上则是“广义”），并且它为绝热参数的所有订单提供了绝热的近似值（通常称为“超级启动”的属性）。除了有限晶格的现有结果外，我们还对绝热扩张进行了重新介绍，并允许观察到并非严格局部。最后，作为一种应用，我们证明了无限系统的扰动类别的线性和高阶响应理论的有效性。 尽管我们认为结果及其证明本身是新颖有趣的，但它们也为仅批量差距的系统的绝热定理提供了基础，这将在后续文章中呈现。
We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalised super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem holds also for certain perturbations of gapped ground states that close the spectral gap (so it is an adiabatic theorem also for resonances and in this sense `generalised'), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called `super-adiabatic'). In addition to existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations also for infinite systems. While we consider the result and its proof as new and interesting in itself, they also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article.
