论文标题
多粒子（相互作用）Aubry-André模型地面定位转换过渡的临界特性
Critical properties of the many-particle (interacting) Aubry-André model ground-state localization-delocalization transition
论文作者
论文摘要
与随机疾病相反，随机疾病将单粒子波函数定位在任意小的障碍强度下的一维障碍中，在有限疾病强度的1D Aubry-André模型中，准周期性疾病的定位转移过渡。在单粒子水平上，通过应用真实的空间重归于组方案来揭示了基态关键行为的许多特性。临界特性仅由疾病不相差频率的持续分数扩展确定。在这里，我们研究了有或没有相互作用的Aubry-André模型中的许多粒子定位 - 偏置转变。与单粒子情况相反，我们发现临界指数取决于与该疾病的不相差频率和填充分数有关的二磷酸方程，这在单粒子频谱中概括了依赖性，这是在单粒子频谱中的持续扩展。在相应的情况下，该方程式可以看作是共振条件的概括。当包括相互作用时，数值证据表明，至少在其中一些关键点可以相互作用，这意味着从二芬太汀方程获得的关键指数关系实际上可以在相互作用的情况下生存。
As opposed to random disorder, which localizes single-particle wave-functions in 1D at arbitrarily small disorder strengths, there is a localization-delocalization transition for quasi-periodic disorder in the 1D Aubry-André model at a finite disorder strength. On the single-particle level, many properties of the ground-state critical behavior have been revealed by applying a real-space renormalization-group scheme; the critical properties are determined solely by the continued fraction expansion of the incommensurate frequency of the disorder. Here, we investigate the many-particle localization-delocalization transition in the Aubry-André model with and without interactions. In contrast to the single-particle case, we find that the critical exponents depend on a Diophantine equation relating the incommensurate frequency of the disorder and the filling fraction which generalizes the dependence, in the single-particle spectrum, on the continued fraction expansion of the incommensurate frequency. This equation can be viewed as a generalization of the resonance condition in the commensurate case. When interactions are included, numerical evidence suggests that interactions may be irrelevant at at least some of these critical points, meaning that the critical exponent relations obtained from the Diophantine equation may actually survive in the interacting case.
