Ultracold atoms in an optical lattice: One-dimensional phase diagram

Abstract

In this project, the ground-state phase diagram of the one-dimensional Extended Bose-Hubbard Model is systematically characterized using the DMRG algorithm via the Julia ITensors library. Benchmark simulations with only on-site interactions, validate the implementation by reproducing the conventional Superfluid to Mott Insulator transition. Incorporating nearest-neighbor interactions at unit filling and employing finite-size scaling at a fixed value of the ratio between on-site interactions and tunneling strength equal to 5, we map three distinct insulating regimes. We confirm that weak nearest-neighbor interactions maintain the Mott phase, while intermediate coupling stabilizes the topological Haldane Insulator, identified by a non-local string order parameter. Finally, strong interactions drive the system into a crystalline Density Wave phase via spontaneous translational symmetry breaking.