## What is/are Kagome Lattices?

Kagome Lattices - , triangular, square, rectangular, honeycomb, and kagome lattices) but also for five nontrivial lattices (i.^{[1]}The model can reasonably be expected to offer quantitative simulations of electron fluid flows in graphene or Kagome lattices.

^{[2]}We investigate the possible regular magnetic order (RMO) for the spin models with global O(3) spin rotation, based on a group theoretical approach for triangular and kagome lattices.

^{[3]}These models can be realized in any lattice that can be tiled by triangles, such as the triangular or kagome lattices, and have been shown to have close connections to the physics of quantum spin liquids in the Heisenberg kagome antiferromagnet.

^{[4]}In particular, we report calculations for Gutzwiller-projected fermionic states on strips of square and kagome lattices.

^{[5]}One particularly interesting nontrivial spin texture existing in several antiferromagnets has spins at an angle of 120° with the in-plane neighbors and arranged in kagome lattices.

^{[6]}We test our method on the ferro and antiferromagnetic Ising model on the two-dimensional square, triangular, honeycomb, and kagome lattices, where we find an excellent agreement with the exact solutions.

^{[7]}In this work we study the interplay of magnons and phonons in honeycomb and Kagome lattices.

^{[8]}By manipulating deposition conditions, diverse assembled architectures have been constructed for Br2Py on Ag(111), including the ladder phase, parallel arrangement, hexagonal patterns from monomers or Kagome lattices based on organometallic (OM) dimers.

^{[9]}Herein, we successfully fabricated two types of Kagome lattices on Cu(111).

^{[10]}The origin of these dispersionless bands, is similar to that of the flat bands in the prototypical Lieb or Kagome lattices and co-exists with the general band flattening at small twist angle due to the moiré interference.

^{[11]}Flat bands have band crossing points with other dispersive bands in many systems including the canonical flat band models in the Lieb and kagome lattices.

^{[12]}We fairly sampled the ground state manifold of square, triangular and Kagome lattices by measuring their coherence function identifying manifolds composed of a single, doubly degenerate, and highly degenerate ground states, respectively.

^{[13]}This paper describes the stepwise formation of kagome lattices of open shell transition metal ions from half-delta chains to delta/sawtooth chains, and finally kagome nets.

^{[14]}Zero-energy topological oppy edge modes have been demonstrated in families of kagome lattices with geometries that differ from the regular case composed of equilateral triangles.

^{[15]}We address previously open key questions — the symmetry actions on monopoles on square, honeycomb, triangular and kagome lattices.

^{[16]}A systematic 3D numerical experiment was conducted for forced convection in a series of isothermally heated sandwich panel structures filled with metal foam, rectangular corrugated cellular structures and various lattice core structures, such as vertical lattices, slanted lattices, Kagome lattices, tetrahedral lattices and pyramidal lattices.

^{[17]}In open crystals, such as the honeycomb and kagome lattices, there is no prominent gap, although soft nonaffine modes continue to be associated with known floppy modes representing localized defects.

^{[18]}In our second application, we find new $Z_2$ spin liquid Hamiltonians on the square and kagome lattices.

^{[19]}In this work, we present a study of the classical Kitaev-Heisenberg model in the pyrochlore and kagome lattices in the highly frustrated regime.

^{[20]}The disparity between the two spatial lengths also has the effect of disrupting the formation of regular patterns leading to irregular and defective hexagons and Kagome lattices.

^{[21]}Motivated by the research interests on realizing flat bands and magnetization plateaus in kagome lattices, we study the electronic properties and magnetic interactions in both zero- and one-dimensional triangular Kagome lattice (1D-TKL) models, by using the real-space Greens function approach in tight-binding model.

^{[22]}Two cases are considered in detail: Lieb and Kagome lattices.

^{[23]}In finite (truncated) Kagome lattices, however, line states cannot preserve as they are no longer the eigenmodes, in sharp contrast to the case of Lieb lattices.

^{[24]}These findings are important for the future search of topological phases in metal-organic networks combining honeycomb and kagome lattices with strong spin-orbit coupling in heavy metal atoms.

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