一维长程Falikov-Kimball模型：热相变和无无序局域化
The one-dimensional Long-Range Falikov-Kimball Model: Thermal Phase Transition and Disorder-Free Localisation
摘要：
无序或相互作用可以使金属变成绝缘体。研究这种物理学的最简单的设置之一是由法利科夫-金博尔模型给出的，该模型描述了巡游费米子与经典伊辛背景场的相互作用。尽管该模型的平移不变性，背景场的非均匀配置引起有效的无序物理，导致丰富的相图在两个（或更多）的维度与有限的温度电荷密度波（CDW）过渡和相互作用调谐安德森与莫特本地化阶段。在这里，我们提出了一个广义的Falikov-Kimball模型在一维长程相互作用，显示了类似的丰富的相图。我们使用一个精确的马尔可夫链蒙特卡罗方法来映射的相图和计算的费米子的能量分辨局域化属性。我们比较这种过渡不变的模型的行为，安德森模型的不相关的二进制障碍的背景CDW场，这证实了费米子部门只完全本地化非常大的系统尺寸。
英文摘要：
Disorder or interactions can turn metals into insulators. One of the simplest settings to study this physics is given by the Falikov-Kimball model, which describes itinerant fermions interacting with a classical Ising background field. Despite the translational invariance of the model, inhomogenous configurations of the background field give rise to effective disorder physics which lead to a rich phase diagram in two (or more) dimensions with finite temperature charge density wave (CDW) transitions and interaction-tuned Anderson versus Mott localized phases. Here, we propose a generalised Falikov-Kimball model in one dimension with long-range interactions which shows a similarly rich phase diagram. We use an exact Markov Chain Monte Carlo method to map the phase diagram and compute the energy resolved localisation properties of the fermions. We compare the behaviour of this transitionally invariant model to an Anderson model of uncorrelated binary disorder about a background CDW field which confirms that the fermionic sector only fully localizes for very large system sizes.
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