Maple leaf antiferromagnet in a magnetic field

We analyze the quantum antiferromagnet on the maple leaf lattice in the presence of a magnetic field. Starting from its exact dimer ground state and for a magnetic field strength of the order of the local dimer spin-exchange coupling, we perform a strong-coupling expansion and extract an effective hard-core boson model. The interplay of effective many-body interactions, suppressed single-particle dynamics, and correlated hopping gives way to an intriguing series of superfluid to insulator transitions which correspond to magnetization plateaus in terms of the maple leaf spin degrees of freedom. While we find plateaus at intermediate magnetization to be dominated by bosonic density wave order, we conjecture plateau formation from multiboson bound states due to correlated hopping for lower magnetization.

Figure 1

Maple leaf model in (1). The dotted blue and thick purple bonds relate to an exchange coupling $J^{\prime }$ and $J$. The six-site unit cell has three dimer sublattices $a,b$, and $c$ (dashed triangle frame). The effective triplet-triplet repulsion (the reference triplet in black) is expanded into pseudopotentials $V_{1,\cdots ,4}$ (3). The bonds related to $V_{1,\cdots ,3}\left(V_4\right)$ unfold from one (three) bond(s) plus lattice symmetry operations.

Figure 2

(a) Hopping of a single triplet (marked by the dimer filled in red) at fourth-order in $J^{\prime }$. There are two symmetry-inequivalent ways a triplet can move between two equal-sublattice dimers. (b) For correlated hopping, one triplet (filled in red) hops assisted by another triplet in its vicinity (filled in black). Such a hopping emerges from second order in $J^{\prime }$ and implies triplet bound states.

Figure 3

(a) The density wave structures at magnetization plateaus. The triplet excitations (singlets) are shown by solid (open) dimers. (b) Magnetization processes of the MLM as a function of $J^{\prime }$ and $h$ up to third order in perturnation.

Figure 4

(a) Two-particle and (c) possible three-particle bound states, and the constituent states with dominant contributions. The solid dimer end points represents a triplet. The light red paralellograms in (a) and (b), and light orange hexagons in (c) and (d) represent the bound states of two and three triplets, respectively. Speculative crystal of (b) two-particle and (d) three-particle bound states giving rise to $m/m_{\text{sat}}=2/19$ and $1/7$. The bound states of two and three triplets are arranged to interact only via $V_4$.