Electronic systems living on Archimedean lattices such as kagome and square-octagon networks are presently being intensively discussed for the possible realization of topological insulating phases. Coining the most interesting electronic topological states in an unbiased way is however not straightforward due to the large parameter space of possible Hamiltonians. A possible approach to tackle this problem is provided by a recently developed statistical learning method [T. Mertz and R. Valentí, Phys. Rev. Research 3, 013132 (2021)], based on the analysis of a large data sets of randomized tight-binding Hamiltonians labeled with a topological index. In this work, we complement this technique by introducing a feature engineering approach which helps identifying polynomial combinations of Hamiltonian parameters that are associated with non-trivial topological states. As a showcase, we employ this method to investigate the possible topological phases that can manifest on the square-octagon lattice, focusing on the case in which the Fermi level of the system lies at a high-order van Hove singularity, in analogy to recent studies of topological phases on the kagome lattice at the van Hove filling.
Breakdown of the thermodynamic limit in quantum spin and dimer models
Joint Quantum Institute, Department of Physics, University of Maryland（马里兰大学联合量子研究所物理系）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（马里兰大学国家标准与技术研究院联合量子信息与计算科学中心）
Observation of square-like moire lattice and quasicrystalline order in twisted rock-salt nitrides
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家实验室）；Department of Physics & Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences（中国科学院大学物理科学与光电技术学院材料科学与光学电子工程中心）；School of information Science and Engineering, Shandong Agricultural University（山东农业大学信息科学与工程学院）；Department of Physics, Southern University of Science and Technology（南方科技大学物理系）
