Simulation of frustrated classical XY models with ultra-cold atoms in 3D triangular optical lattices

TL;DR

This paper explores the simulation of frustrated classical XY models using ultra-cold atoms in 3D triangular optical lattices, analyzing phase diagrams, stability, and potential realizations in optical lattice systems.

Contribution

It introduces a detailed simulation framework for frustrated XY models in 3D optical lattices, including phase analysis and stability, with proposals for experimental realization.

Findings

Analysis of phase diagram and dynamical stability.

Proposal for realizing complex tunneling in optical lattices.

Discussion of symmetry-breaking in tunneling amplitudes.

Abstract

Miscellaneous magnetic systems are being recently 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.