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

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.

27 pages, 14 figures

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Cited by in corpus (7)

• Dynamic freezing and defect suppression in the tilted one-dimensional Bose-Hubbard model
• Ramp and periodic dynamics across non-Ising critical points
• Tuning towards dynamic freezing using a two-rate protocol
• Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning
• Spin-models, dynamics and criticality with atoms in tilted optical superlattices
• Mott-insulator state of cold atoms in tilted optical lattices: doublon dynamics and multi-level Landau-Zener tunneling
• Generalized effective-potential Landau theory for the two-dimensional extended Bose-Hubbard model