Quantum many particle systems in which the kinetic energy, strong correlations, and band topology are all important pose an interesting and topical challenge. Here we introduce and study particularly simple models where all of these elements are present. We consider interacting quantum particles in two dimensions in a strong magnetic field such that the Hilbert space is restricted to the Lowest Landau Level (LLL). This is the familiar quantum Hall regime with rich physics determined by the particle filling and statistics. A periodic potential with a unit cell enclosing one flux quantum broadens the LLL into a Chern band with a finite bandwidth. The states obtained in the quantum Hall regime evolve into conducting states in the limit of large bandwidth. We study this evolution in detail for the specific case of bosons at filling factor $ν= 1$. In the quantum Hall regime the ground state at this filling is a gapped quantum hall state (the "bosonic Pfaffian") which may be viewed as descending from a (bosonic) composite fermi liquid. At large bandwidth the ground state is a bosonic superfluid. We show how both phases and their evolution can be described within a single theoretical framework based on a LLL composite fermion construction. Building on our previous work on the bosonic composite fermi liquid, we show that the evolution into the superfluid can be usefully described by a non-commutative quantum field theory in a periodic potential.
Scrutinizing Hall effect in Mn$_{1-x}$Fe$_{x}$Si: Fermi surface evolution and hidden quantum criticality
区分Mn $_{1-x}$ Fe $_{x}$ Si顺磁相中的正常（OHE）和异常（AHE）霍尔效应揭示了与隐藏的量子临界（QC）点$x^*\sim0.11$相关的OHE符号反转。在中等Fe含量下的半金属行为导致Mn $_{1-x}$ Fe $_{x}$ Si中的费米学、磁相互作用和QC领域中的可验证的预测。电子和空穴浓度的变化被认为是通过修改海森堡磁性模型中的RKKY交换相互作用来调节Mn $_{1-x}$ Fe $_{x}$ Si中QC区域的驱动力。
