Murad Tovmasyan, Sebastiano Peotta, Long Liang, Päivi Törmä, Sebastian D. Huber
备注：
24 pages, 10 figures. This version version is almost identical to the published one. Some minor errors present in the published version have been corrected here
In a flat Bloch band the kinetic energy is quenched and single particles cannot propagate since they are localized due to destructive interference. Whether this remains true in the presence of interactions is a challenging question because a flat dispersion usually leads to highly correlated ground states. Here we compute numerically the ground state energy of lattice models with completely flat band structure in a ring geometry. We find that the energy as a function of the magnetic flux threading the ring has a half-flux quantum $Φ_0/2 = hc/(2e)$ period, indicating that only bound pairs of particles with charge $2e$ are propagating, while single quasiparticles with charge $e$ remain localized. We show analytically in one dimension that in fact the whole many-body spectrum has the same periodicity. Our analytical arguments are valid for both bosons and fermions, for generic interactions respecting some symmetries of the lattice and at arbitrary temperatures. Moreover we construct an extensive number of exact conserved quantities for the one dimensional lattice models. These conserved quantities are associated to the occupation of localized single quasiparticle states. Our results imply that in lattice models with flat bands preformed pairs dominate transport even above the critical temperature of the transition to a superfluid state.
Designing flat-band tight-binding models with tunable multifold band touching points
周期晶格上的平坦带是无色散的，其唯一特征在于它们的宏观简并本征态：实空间中的紧凑局域态（CLS）和倒易空间中的布洛赫态。基于这一性质，本文提出了一种简单的方法来建立具有短程跳跃的平带紧束缚模型\emph{on any periodic lattice}。该方法包括在从CLS和工程家庭的布洛赫哈密顿作为相关的布洛赫状态的二次（或线性）函数。由此产生的紧束缚模型不仅表现出一个平坦的带，但也多重二次（或线性）带接触点（BTP）的数量，位置和简并可以在很大程度上控制。二次平带模型是普遍存在的：它们可以从任意CLS构建，在任何晶格上，在任何维度上，具有任何数量的带$N\geq2$。线性平带模型比较罕见：它们需要$N\geq3$，并且只能从满足与底层晶格的某些兼容关系的CLS构建。文献中的大多数平带模型都可以根据这个方案进行分类：Mielke和Tasaki的模型属于二次类，而Lieb，Dice和呼吸Kagome模型属于线性类。介绍了许多新的平带模型，其中包括四阶二次带点的$N=4$双层蜂窝模型、五阶线性带点的$N=5$骰子模型和带点从线性到二次平滑调谐的$N=3$ Kagome模型.
Fractional Chern Insulators Transition in Non-ideal Flat Bands of Twisted Mono-bilayer Graphene
State Key Laboratory of Semiconductor Physics and Chip Technologies, Institute of Semiconductors, Chinese Academy of Sciences（中国科学院半导体研究所半导体物理与芯片技术国家重点实验室）；Center for Quantum Matter, Zhejiang University（浙江大学量子物质中心）；College of Materials Science and Opto-electronic Technology, University of Chinese Academy of Sciences（中国科学院大学材料科学与光电技术学院）
Identifying Instabilities with Quantum Geometry in Flat Band Systems
French American Center for Theoretical Science, CNRS（法国美国理论科学中心，法国国家科学研究中心）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；Canadian Institute for Advanced Research（加拿大高级研究院）
General Construction from Topological Loop States to Topological Invariants in Exactly Flat Bands
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）；University of Chinese Academy of Sciences（中国科学院大学）；New Cornerstone Science Laboratory（新 cornerstone 科学实验室）
The University of Tokyo（东京大学）；The University of Osaka（大阪大学）；Kyoto University（京都大学）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所涌现物质科学中心）；Hiroshima University（广岛大学）
Tracking flat bands via phonon-mediated interband scattering
Materials Physics Applications–Quantum, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究所）；Institute of Solid State Physics, TU Wien（维也纳工业大学固体物理研究所）
Fractional quantization by interaction of arbitrary strength in gapless flat bands with divergent quantum geometry
HK Institute of Quantum Science & Technology, The University of Hong Kong（香港量子科学及技术研究院，香港大学）；State Key Laboratory of Optical Quantum Materials, The University of Hong Kong（光学量子材料国家重点实验室，香港大学）
