Abstract
We study spinless bosons in a decorated square lattice with a near-diagonal
tilt. The resonant subspace of the tilted Mott insulator is described by an
effective Hamiltonian of frustrated quantum Ising spins on a non-bipartite
lattice. This generalizes an earlier proposal for the unfrustrated quantum
Ising model in one dimension which was realized in a recent experiment on
ultracold \$^87\$Rb atoms in an optical lattice. Very close to diagonal tilt,
we find a quantum liquid state which is continuously connected to the
paramagnet. Frustration can be reduced by increasing the tilt angle away from
the diagonal, and the system undergoes a transition to an antiferromagnetically
ordered state. Using quantum Monte Carlo simulations and exact diagonalization,
we find that for realistic system sizes the antiferromagnetic order appears to
be quasi-one-dimensional; however, in the thermodynamic limit the order is
two-dimensional.
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