Artificial gauge-fields in the Bose-Hubbard model on the triangular lattice

Shaking the triangular optical lattice with an extra potential at a resonant frequency can provide different artificial gauge-fields (e.g. complex phases of the tunneling matrix elements between two neighbor lattice sites) along three inequivalent axes. We systematically study the phase diagram of the artificially gauged Bose-Hubbard model on the triangular lattice by using large-scale two-dimensional density-matrix renormalization group (DMRG) method, infinite-DMRG method and also the process-chain algorithm of the strong-coupling expansion. The numerical results self-consistently point out that the artificial gauge-field strongly affect the type of the transitions from the Mott-insulating phase to the superfluid phase. Especially, the transition becomes discontinuous at high-symmetry points because of breaking a topological discrete symmetry. Other properties of criticality are discussed.