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 $\rho$ = 2/3, and superfluid phases between solid phases.Two ways of controlling quantum states are discussed: to add an alternating on-site $\mu$ potential, and to add an alternating hopping amplitude in the X- and Y-directions. For the above cases, there exists a new filling state, $\rho$ = 1/3. Adding an alternating on-site potential to the Hamiltonian, the phase transition from $\rho =1/3$ to $\rho =2/3$ 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 $\rho =0$ and lower boundary for $\rho =1$ are calculated.