Numerical simulations of dimensional-crossover- and frustration-driven phenomena in correlated electron systems -- renewal proposal

在第一个资助期的基础上，我们打算进一步研究维数和挫折对量子自旋和相关电子系统中涌现现象的影响。操纵金属表面上的磁性附着原子的能力为设计和探索近藤纳米系统开辟了新的途径。具体来说，我们将讨论产生近藤晶格极限固有特征的可行性——重费米子金属丰度和部分近藤筛选，由杂质位点的常规耗尽或经典挫败引起。另一个与实验相关的问题涉及层状近藤异质结构中磁性有序-无序转变的性质。我们的下一个目标是阐明具有可变层数的SU(N)量子反铁磁体中Berry相的相关性及其对量子相变的影响。作为一个有趣的新研究方向，我们将研究双通道Kondo模型（即Majorana模式）的奇异局部激发是否以及如何在维度交叉时获得色散。对于上述所有研究项目，我们将使用基于有限温度和零温度下辅助场量子蒙特卡罗（QMC）算法和/或连续时间QMC方法的无偏数值技术。

Building on the results from the first funding period, we intend to further study the impact of dimensionality and frustration on the emergent phenomena in quantum spin and correlated electron systems. The ability to manipulate magnetic adatoms on metallic surfaces opens up new avenues to design and explore Kondo nanosystems. Specifically, we shall address the feasibility of generating features inherent to the Kondo lattice limit --- heavy-fermion metallicity and partial Kondo screening, induced either by a regular depletion of the impurity sites or classical frustration. Another experimentally relevant question concerns the nature of a magnetic order-disorder transition in layered Kondo heterostructures. Our next goal is to elucidate the relevance of Berry phases and their impact on the quantum phase transition in SU(N) quantum antiferromagnets with a variable number of layers. As an interesting novel research direction we will investigate if and how the exotic local excitations of the two-channel Kondo model, i.e., a Majorana mode, can acquire dispersion upon dimensional crossover. For all the above research projects, we will use unbiased numerical techniques based on the auxiliary field quantum Monte Carlo (QMC) algorithm at finite and zero temperature and/or the continuous-time QMC method.