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The $\alpha$-$T_3$ model extrapolates between the pseudospin $S=1/2$ honeycomb lattice of graphene and the pseudospin $S=1$ dice… Expand Chern numbers characterize the quantum Hall effect conductance—non-zero values are associated with topological phases. Previously… Expand We rely on a recent method for determining edge spectra and we use it to compute the Chern numbers for Hofstadter models on the… Expand We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of… Expand The Hofstadter butterfly spectral patterns of lattice electrons in an external magnetic field yield some of the most beguiling… Expand The electronic spectrum of a two-dimensional square lattice in a perpendicular magnetic field has become known as the Hofstadter… Expand We investigate the dynamics of neutral atoms in a 2D optical lattice which traps two distinct internal states of the atoms in… Expand Conceptual integration—“blending”—is a general cognitive operation on a par with analogy, recursion, mental modeling, conceptual… Expand concept (as opposed to the instance thereof found inside the string xyz). Many people, eager to construct a successor to Platonic… Expand Abstract We study integrable vertex models and quantum spin chains with toroidal boundary conditions. An interesting class of… Expand