Superfluidity in the 1D Bose-Hubbard Model

Due to strong quantum fluctuations, superfluidity in one dimension is special: The superfluid state is critical, with power-law-decaying correlation functions and no Bose-Einstein condensation. In a lattice, where one can find an interaction-driven Mott insulator, the physics is even more interesting. We compute the ground state superfluid density of the 1D Bose-Hubbard model using an infinite variational matrix product state technique. We explore the scaling relationships involving the correlation functions and entanglement entropy, explicitly demonstrating the connection between superfluid density and Luttinger parameters. We compare two different algorithms for optimizing the infinite matrix product state and develop a physical explanation why one of them (VUMPS) is more efficient than the other (iDMRG).