The Numerical Renormalization Group applied to the Bose Hubbard Model

Steven R. White

Osamu Sakai, Yoshio Kuramoto

Jesús Pérez-Conde

C.-H. Pao, H.-B. Schüttler

Pallavi P. Gaude, Ananya Das, Ramesh V. Pai

Abstract The cluster mean-field with density matrix renormalization (CMFT + DMRG) method which combines the simplicity of the mean-field theory and the numerical power of the density-matrix renormalization group method is applied to understand the quantum phases of the one-dimensional Bose–Hubbard models. We show that the CMFT + DMRG method is an effective numerical technique with moderate computational resources to determine relevant order parameters and correlation functions of large one-dimensional systems. We apply the CMFT + DMRG for the Bose Hubbard and extended Bose Hubbard models to account for the superfluid, Mott insulator, and density wave phases in these models. Our results are in good agreement with the known phase diagram of these models, demonstrating the efficacy of this method.

Mateusz Łącki, Bogdan Damski, Jakub Zakrzewski

We compute ground-state fidelity of the one-dimensional Bose-Hubbard model at unit filling factor. To this aim, we apply the density matrix renormalization group algorithm to systems with open and periodic boundary conditions. We find that fidelity differs significantly in the two cases and study its scaling properties in the quantum critical regime.