Abstract:
In this thesis, we study the ground-state phases of an extended Bose-Hubbard ladder using the density-matrix renormalization group (DMRG) algorithm. Each chain in the ladder is characterized by an onsite interaction U, nearest-neighbor interaction V, and intrachain hopping J comprising an extended Bose-Hubbard model (EBHM). Though the ground-state phases of a single chain EBHM are well understood, the ladder remains completely unexplored. We assume that the chains in the ladder are coupled through the hopping of atoms in the rungs, and we explore how it affects the current phase diagram of a single chain. We use charged-energy gap, density-wave order, and
non-local string order to identify the ground state phases.
Further, we use finite-size scaling to estimate the phase boundaries of the thermodynamic limit. Restricting the analysis to a unit filling factor, we find that a supersolid state emerges in the phase diagram due to the inter-chain hopping. In particular, the supersolid (SS) state is sandwiched between the superfluid (SF) and the density wave (DW). Interestingly, the emergence of SS is accompanied by a reentrant behavior at which the system undergoes SS-DW-SS transition as a function of the contact interaction strength (U). Other states such as Mott-insulator and Haldane insulator may arise depending on the onsite interaction strength or boundary conditions.
We provide a comprehensive picture of the role of inter-chain tunneling on the ground state properties by calculating the superfluid correlation, rung correlation, rung-rung correlation, rung-leg correlation, and entanglement. Further, we show that removing a single rung in the ladder may have drastic effects on the phase diagram. We propose two realistic setups based on dipolar atoms/polar molecules and Rydberg-dressed atoms loaded in optical lattices for implementing the symmetric Bose-Hubbard ladder. Our studies open up various directions in the physics of the Bose-Hubbard ladder. For instance, one can investigate the effect of hopping in a multi-leg ladder or the quantum quench dynamics through the reentrant region, including the Kibble-Zurek mechanism.
