Engineering Quantum Phases of Ultracold Bosons on Lieb Lattice

Abstract The quantum phase transition of the hardcore boson model on a Lieb lattice by quantum Monte Carlo simulations is studied. Considering nearest‐neighbor interchain hopping, the phase diagram of the Bose‐Hubbard model on the Lieb lattice contains solid phases with average density = 2/3, and superfluid phases between solid phases.Two ways of controlling quantum states are discussed: to add an alternating on‐site potential, and to add an alternating hopping amplitude in the X ‐ and Y ‐directions. For the above cases, there exists a new filling state, = 1/3. Adding an alternating on‐site potential to the Hamiltonian, the phase transition from to is sharp and discontinuous, featuring the nature of a first order. Considering a dimerization term, for large V, it is expected that there is a direct transition from the valence‐bond insulator to the CDW as the interaction is strengthened. For the three cases, upper boundary for and lower boundary for are calculated.