Dynamic properties of the one-dimensional Bose-Hubbard model

Abstract

We use the density-matrix renormalization group method to investigate ground-state and dynamic properties of the one-dimensional Bose-Hubbard model, the effective model of ultracold bosonic atoms in an optical lattice. For fixed maximum site occupancy $n_b=5$, we calculate the phase boundaries between the Mott insulator and the `superfluid' phase for the lowest two Mott lobes. We extract the Tomonaga-Luttinger parameter from the density-density correlation function and determine accurately the critical interaction strength for the Mott transition. For both phases, we study the momentum distribution function in the homogeneous system, and the particle distribution and quasi-momentum distribution functions in a parabolic trap. With our zero-temperature method we determine the photoemission spectra in the Mott insulator and in the `superfluid' phase of the one-dimensional Bose-Hubbard model. In the insulator, the Mott gap separates the quasi-particle and quasi-hole dispersions. In the `superfluid' phase the spectral weight is concentrated around zero momentum.

6 pages, 7 figures

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• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Transition from a strongly interacting 1D superfluid to a Mott insulator
• Quantum phases in an optical lattice
• The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction
• Dynamical density-matrix renormalization-group method
• Strong-coupling expansions for the pure and disordered bose Hubbard model
• Phases of the one-dimensional Bose-Hubbard model
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Extension of Bogoliubov theory to quasi-condensates
• Mott Domains of Bosons Confined on Optical Lattices
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• Dynamics and Thermodynamics of the Bose-Hubbard model
• Phase diagram of the one-dimensional half-filled extended Hubbard model
• Spatial correlations of trapped 1d bosons in an optical lattice
• Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results
• Tomonaga-Luttinger parameters for doped Mott insulators
• Spectral weight redistribution in strongly correlated bosons in optical lattices
• Exact prefactors in static and dynamic correlation functions of 1D quantum integrable models: applications to the Calogero-Sutherland, Lieb-Liniger and XXZ models
• Excitation spectra of strongly correlated lattice bosons and polaritons
• Process chain approach to the Bose-Hubbard model: Ground-state properties and phase diagram
• Loop updates for quantum Monte Carlo simulations in the canonical ensemble
• Interacting bosons in an optical lattice
• The Mott insulator phase of the one dimensional Bose-Hubbard model: a high order perturbative study
• Variational Cluster Perturbation Theory for Bose-Hubbard models
• Critical exponents of the degenerate Hubbard model
• Accurate determination of the superfluid-insulator transition in the one-dimensional Bose-Hubbard model

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