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Chinese Physics Letters

Ground State Property of a One-Dimensional Bose—Hubbard Model Using Time-Evolving Body Decimation

Sheng-De Ouyang, Jing Liu, Shao-Hua Xiang, Kehui Song

Published Aug 1, 2013• 1 citation
Publisher

Abstract

We study the ground state property of the one-dimensional Bose—Hubbard model using an imaginary time evolving body decimation algorithm. The single-particle density matrix is numerically calculated for a Mott insulating system and a superfluid system separately. By plotting the chemical potential versus the filling n = N/L for U/J = 20 and U/J = 0.1, we identify the Mott gap for U/J = 20 in filling n = 1. Lastly, we investigate the occupation number of the Bloch state with quasimomentum for a system deep in the Mott phase and in the superfluid phase respectively. The results indicate Bose condensation in the quasimomentum space.

DOI
10.1088/0256-307x/30/8/086701

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We study the ground state property of the one-dimensional Bose—Hubbard model using an imaginary time evolving body decimation algorithm. The single-particle density matrix is numerically calculated for a Mott insulating system and a superfluid system separately. By plotting the chemical potential versus the filling n = N/L for U/J = 20 and U/J = 0.1, we identify the Mott gap for U/J = 20 in filling n = 1. Lastly, we investigate the occupation number of the Bloch state with quasimomentum for a system deep in the Mott phase and in the superfluid phase respectively. The results indicate Bose condensation in the quasimomentum space.
We study the quantum phase transition between the superfluid and the Mott insulator in the one-dimensional (1D) Bose-Hubbard model. Using the time-evolving block-decimation method, we numerically calculate the tunneling splitting of two macroscopically distinct states with different winding numbers. From the scaling of the tunneling splitting with respect to the system size, we determine the critical point of the superfluid-to-Mott-insulator transition for arbitrary integer filling factors. We find that the critical values versus the filling factor in 1D, 2D, and 3D are well approximated by a simple analytical function. We also discuss the condition for determining the transition point from a perspective of the instanton method.
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.
The one-dimensional extended bosonic Hubbard model has been shown to exhibit a variety of phases ranging from Mott insulator and superfluid to exotic supersolids and Haldane insulators depending on the filling and the relative value of the contact (UUU) and near neighbor (VVV) interaction strengths. In this paper we use the density matrix renormalization group and the time evolving block decimation numerical methods to study in detail the dynamics and excitation spectra of this model in its various phases. In particular, we study in detail the behavior of the charge and neutral gaps which characterize the Mott, charge density, and Haldane insulating phases. We also show that in addition to the gapless modes at k=0k=0k=0, the supersolid phase exhibits gapless modes at a finite kkk which depends on the filling.
We determine the ground-state properties of a gas of interacting bosonic atoms in a one-dimensional optical lattice. The system is modeled by the Bose-Hubbard Hamiltonian. We show how to apply the time-evolving block decimation method to systems with periodic boundary conditions and employ it as a reference to find the ground state of the Bose-Hubbard model. Results are compared with recently proposed approximate methods, such as Hartree-Fock-Bogoliubov (HFB) theories generalized for strong interactions and the variational Bijl-Dingle-Jastrow method. We find that all HFB methods do not bring any improvement to the Bogoliubov theory and therefore provide correct results only in the weakly interacting limit, where the system is deeply in the superfluid regime. On the other hand, the variational Bijl-Dingle-Jastrow method is applicable for much stronger interactions but is essentially limited to the superfluid regime as it reproduces the superfluid--Mott-insulator transition only qualitatively.
We investigate the interaction-induced superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings n=1n=1n=1, n=2n=2n=2, and n=3n=3n=3 by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.