Quantum Phases and Transitions of Bosons on a Comb Lattice

Motivated to elucidate the nature of quantum phases and their criticality when entangled with a correlated quantum bath, we study interacting bosons on a "comb lattice"-a one-dimensional backbone (system) coupled at its sites to otherwise independent one-dimensional "teeth" chains (bath). We map out the corresponding phase diagram, detailing the nature of the phases and phase transitions. Controlled by the backbone and teeth hopping amplitudes, short-range interactions, and chemical potential, phases include a Mott insulator, backbone, and teeth Luttinger liquids and the long-range ordered incoherent superfluid. We explore their properties and potential realizations in condensed matter and cold-atom experiments and simulations.