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

Frustrated quantum Ising spins simulated by spinless bosons in a tilted lattice: from a quantum liquid to antiferromagnetic order