  The study of geometrically frustrated many-body quantum systems is of central
importance to uncover novel quantum mechanical effects. We design a scheme
where ultracold bosons trapped in a one-dimensional state-dependent optical
lattice are modeled by a frustrated Bose-Hubbard Hamiltonian. A derivation of
the Hamiltonian parameters based on Cesium atoms, further show large tunability
of contact and nearest-neighbour interactions. For pure contact repulsion, we
discover the presence of two phases peculiar to frustrated quantum magnets: the
bond-order-wave insulator with broken inversion symmetry and a chiral
superfluid. When the nearest-neighbour repulsion becomes sizeable, a further
density-wave insulator with broken translational symmetry can appear. We show
that the phase transition between the two spontaneously-symmetry-broken phases
is continuous, thus representing a one-dimensional deconfined quantum critical
point not captured by the Landau-Ginzburg-Wilson symmetry-breaking paradigm.
Our results provide a solid ground to unveil the novel quantum physics induced
by the interplay of non-local interactions, geometrical frustration, and
quantum fluctuations.
