Magnetism plays a key role in modern technology and stimulates research in several branches of condensed matter physics. Although the theory of classical magnetism is well developed, the demonstration of a widely tunable experimental system has remained an elusive goal. Here, we present the realization of a large-scale simulator for classical magnetism on a triangular lattice by exploiting the particular properties of a quantum system. We use the motional degrees of freedom of atoms trapped in an optical lattice to simulate a large variety of magnetic phases: ferromagnetic, antiferromagnetic, and even frustrated spin configurations. A rich phase diagram is revealed with different types of phase transitions. Our results provide a route to study highly debated phases like spin-liquids as well as the dynamics of quantum phase transitions.
Miscellaneous magnetic systems are currently being intensively investigated because of their potential applications in modern technologies. Nonetheless, a many-body dynamical description of complex magnetic systems may be cumbersome, especially when the system exhibits a geometrical frustration. This paper deals with simulations of the classical
XY model on a three-dimensional triangular lattice with anisotropic couplings, including an analysis of the phase diagram and a Bogoliubov description of the dynamical stability of mean-field stationary solutions. We also discuss the possibilities of the realization of Bose-Hubbard models with complex tunneling amplitudes in shaken optical lattices without breaking the generalized time-reversal symmetry and the opposite, i.e., real tunneling amplitudes in systems with the time-reversal symmetry broken.
Quantum simulators based on cold atomic gases can provide an ideal platform to study the microscopic mechanisms behind intriguing properties of solid materials and further explore novel exotic phenomena inaccessible by chemical synthesis. Here we propose and theoretically analyze a coherently coupled binary mixture of Fermi atoms in a triangular optical lattice as a promising realization of synthetic frustrated antiferromagnets. We perform a cluster mean-field plus scaling analysis to show that the ground state exhibits several nontrivial magnetic phases and a novel spin reorientation transition caused by the quantum order-by-disorder mechanism. Moreover, we find from Monte Carlo simulations that thermal fluctuations induce an unexpected coexistence of Berezinskii-Kosterlitz-Thouless physics and long-range order in different correlators. These predictions, besides being relevant to present and future experiments on triangular antiferromagnetic materials, can be tested in the laboratory with the combination of the currently available techniques for cold atoms.