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

TL;DR

This paper investigates frustrated quantum Ising spins simulated by spinless bosons in a tilted lattice, revealing a transition from a quantum liquid to antiferromagnetic order, with insights from simulations on finite and infinite systems.

Contribution

It introduces an effective Hamiltonian for frustrated quantum Ising spins in a tilted lattice, extending previous unfrustrated models and exploring phase transitions using numerical methods.

Findings

Identification of a quantum liquid state near diagonal tilt.

Observation of a transition to antiferromagnetic order with increased tilt.

Finite-size simulations suggest quasi-one-dimensional order, but true two-dimensional order in the thermodynamic limit.

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.