Dynamic properties of the one-dimensional Bose-Hubbard model

TL;DR

This paper investigates the ground-state and dynamic properties of the one-dimensional Bose-Hubbard model using density-matrix renormalization group, focusing on phase boundaries, correlation functions, and spectral features.

Contribution

It provides precise calculations of phase boundaries, critical interaction strengths, and spectral properties for the 1D Bose-Hubbard model, including effects of a trapping potential.

Findings

Determined phase boundaries between Mott insulator and superfluid phases.

Extracted the Tomonaga-Luttinger parameter from correlation functions.

Calculated photoemission spectra showing Mott gap and spectral weight distribution.

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.