Pielawa, SusanneBerg, ErezSachdev, Subir2013-07-252012Pielawa, Susanne, Erez Berg, and Subir Sachdev. 2012. Frustrated quantum Ising spins simulated by spinless bosons in a tilted lattice: From a quantum liquid to antiferromagnetic order. Physical Review B 86(18): 184435.1098-0121http://nrs.harvard.edu/urn-3:HUL.InstRepos:10885507We 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 nonbipartite 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.en-USquantum gasesJournal Article2013-07-2510.1103/PhysRevB.86.184435