One-Dimensional Disordered Bosonic Hubbard Model: A Density-Matrix Renormalization Group Study

Abstract

We use the density-matrix renormalization group to study the one-dimensional bosonic Hubbard model, with and without disorder. We obtain the gaps in all phases, certain correlation functions, and the superfluid density. A finite-size-scaling analysis enables us to obtain an accurate phase diagram and the b function at the superfluid-Mott insulator transition and the Kosterlitz-Thouless essential singularity in the pure case. We also obtain coupling constants used in effective field theories for this system.

The one-dimensional extended Bose-Hubbard model

“…2,5,[7][8][9][10][11] In particular, if V = 0 and there is no disorder, only an SF phase is obtained at noninteger densities. For integer densities an MI phase is obtained at large U; as U is lowered the system shows an MI-SF transition, which is of the Kosterlitz-Thouless type 23 in one dimension.…”

“…7,24 For our purposes here it suffices to note that, especially in one dimension and with open boundary conditions, the DMRG method allows us to calculate the ground-state energy…”

“…The most detailed study of this transition in the Bose-Hubbard model was carried out by us in Ref. [7] by using the DMRG method.…”

“…However, especially in low dimensions, such mean-field theories cannot always uncover the types of correlations present in these phases or the natures of the transitions between these phases. We have shown earlier 7 that, for one-dimensional Bose-Hubbard models, the density-matrix-renormalization-group (DMRG) is a reliable method for the elucidation of such correlations and the universality classes of quantum phase transitions. Here we give a brief overview of our recent calculation of the zero-temperature phase diagram of the extended-Bose-Hubbard model in one dimension by the DMRG method.…”

“…The latter include studies of liquid 4 He in porous media like vycor or aerogel, 15 Bose-Einstein condensates trapped in optical lattices, 16,17 micro-fabricated Josephson-junction arrays, 18-20 the disorder-driven superconductor-insulator transition in thin films of superconducting materials like bismuth, 21 and flux lines in type-II superconductors pinned by columnar defects aligned with the external magnetic field. 22 Theoretical and numerical studies [2][3][4]7,11,12 have concentrated on the Bose-Hubbard model which exhibits superfluid (SF) and bosonicMott-insulator (MI) phases and, if onsite disorder is included, a Bose-glass (BG) phase too. As we will show below, a mass-density-wave (MDW) phase can also be obtained in an extended-Bose-Hubbard model.…”