热力学极限下的绝热定理：具有均匀能隙的系统
Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap
AI总结：
本研究证明有限格点有相互作用有隙多体系统的绝热理论结果在热力学极限下成立，提出推广的超绝热定理，拓展了可观测量适用范围，还验证了无穷系统的响应理论，为后续体相有隙系统的绝热定理研究奠基。
摘要：
我们证明，近期关于有限格点上有相互作用的有隙多体系统的绝热理论结果，在热力学极限下依然成立。更确切地说，我们针对描述可观测量准局域代数上无穷体积动力学的自同构群，证明了一个推广的超绝热定理。核心假设是存在一列有隙的有限体积哈密顿量，该序列在热力学极限下生成相同的无穷体积动力学。我们的绝热定理同样适用于会闭合谱隙的有隙基态的特定微扰（因此它也是适用于共振态的绝热定理，在此意义上是“推广的”），并且它能给出绝热参数任意阶的绝热近似（这一性质常被称为“超绝热”）。除了已有的有限格点相关结果外，我们还对绝热展开进行了重求和，并且允许使用非严格局域的可观测量。最后，作为一项应用，我们证明了线性及更高阶响应理论对于我们这类微扰也适用于无穷系统。虽然我们认为该结果及其证明本身就具有新颖性和研究价值，但它们也为仅在体相中存在能隙的系统的绝热定理证明奠定了基础，相关内容将在后续论文中呈现。
英文摘要：
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.
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