Staircase of crystal phases of hard-core bosons on the kagome lattice

Abstract

We study the quantum phase diagram of a system of hard-core bosons on the Kagome lattice with nearest-neighbor repulsive interactions, for arbitrary densities, by means of the hierarchical mean field theory and exact diagonalization techniques. This system is isomorphic to the spin S=1/2 XXZ model in presence of an external magnetic field, a paradigmatic example of frustrated quantum magnetism. In the non-frustrated regime, we find two crystal phases at densities 1/3 and 2/3 that melt into a superfluid phase when increasing the hopping amplitude, in semi-quantitative agreement with quantum Monte Carlo computations. In the frustrated regime and away from halffilling, we find a series of plateaux with densities commensurate with powers of 1/3. The broader density plateaux (at densities 1/3 and 2/3) are remnants of the classical degeneracy in the Ising limit. For densities near half-filling, this staircase of crystal phases melts into a superfluid, which displays finite chiral currents when computed with clusters having an odd number of sites. Both the staircase of crystal phases and the superfluid phase prevail in the non-interacting limit, suggesting that the lowest dispersionless single-particle band may be at the root of this phenomenon.

Magnetization plateau observed by ultrahigh-field Faraday rotation in the kagome antiferromagnet herbertsmithite

“…The interaction J of herbertsmithite is reported to be around 180-300 K 8,19,20 , from which the saturation field is evaluated as 3J = 400 T-600 T. Therefore, the magnetization kink above Bp cannot be caused by full moment saturation but is most likely due to the 1/3 magnetization plateau. This can also be inferred from the theoretical prediction that the plateau starts to appear above B ~ J [28][29][30][31][32][33]47 . A comparison of various theoretical models and our experiment results is presented in Fig.…”

“…A striking feature of the kagomé antiferromagnet is that the magnon does not propagate but resonates inside a hexagon 27 . Below the saturation field, such hexagonal magnons condense into a series of crystalline states in the absence of quenched disorder [27][28][29][30][31][32][33] . Experimentally, these can be observed as 1/3, 5/9, and 7/9 magnetization plateaus on the magnetization curve.…”

Quantum phases of Rydberg atoms on a kagome lattice

“…In the classical limit of δ/Ω → ∞, the periodic arrangement of Rydberg excitations (or equivalently hard-core bosons) on the kagome lattice can result in additional ordered phases besides the nematic and the staggered ones at various fractional densities (41). To see this, one can simply minimize the classical energy, which is determined solely by the competition between the detuning and the repulsive interactions.…”

Kinetic frustration induced supersolid in the S=12 kagome lattice antiferromagnet in a magnetic field

“…In the following, we will not discuss the small plateau at m = 1/9, whose nature is still unclear. 46,48,55 There are several numerical evidences that the other plateaus at m = 3/9, 5/9, 7/9 host crystals which all have the same symmetry breaking of an extended nine-site unit, called √ 3 × √ 3 structure. 43,44,48 A schematic picture of those crystals is given in Fig.…”