Computational Methods for Low-Lying Excitations in the Hubbard Model and Superfluid Helium

Low-lying excitations of ${}^{4}$ He and ${}^{3}$ He atoms confined inside zeolite cages have been modeled by Bose-Hubbard and Mott-Hubbard rings with strong intrasite repulsion and finite intersite attraction. Differences between ${}^{4}$ He and ${}^{3}$ He arise due to mass and the statistics. Calculated temperature and concentration dependences of the heat capacity agree qualitatively with the experiment, but a quantitative comparison suggests that disorder may dominate at very low $T$ .Low-lying excitations of ${}^{4}$He and ${}^{3}$He atoms confined inside zeolite cages have been modeled by Bose-Hubbard and Mott-Hubbard rings with strong intrasite repulsion and finite intersite attraction. Differences between ${}^{4}$He and ${}^{3}$He arise due to mass and the statistics. Calculated temperature and concentration dependences of the heat capacity agree qualitatively with the experiment, but a quantitative comparison suggests that disorder may dominate at very low $T$.

Physical Review LettersJul 17, 199556 citations

Quantum simulation of the 2D Hubbard model

Michael Köhl

Bulletin of the American Physical SocietyJun 8, 20170 citations

Excitation Spectra of Correlated Lattice Bosons in a Confining Trap

Dmitry L. Kovrizhin, G. Venketeswara Pai, Subhasis Sinha

We consider ultracold bosonic atoms in an optical lattice with an external trapping potential. To study the excitation energies of the resulting Bose-Hubbard model, we develop a method based on a time-dependent generalization of the Gutzwiller ansatz. We calculate the excitations of the homogeneous system both in insulating and superfluid regime, concentrating particularly on those near the superfluid-Mott insulator boundary. Low-lying excitation energies in presence of a static harmonic trap are obtained using this method and compared with the homogeneous case. Further, we explore the dynamics of the center of mass and the breathing mode in response to time-dependent perturbations of the trap.We consider ultracold bosonic atoms in an optical lattice with an external trapping potential. To study the excitation energies of the resulting Bose-Hubbard model, we develop a method based on a time-dependent generalization of the Gutzwiller ansatz. We calculate the excitations of the homogeneous system both in insulating and superfluid regime, concentrating particularly on those near the superfluid-Mott insulator boundary. Low-lying excitation energies in presence of a static harmonic trap are obtained using this method and compared with the homogeneous case. Further, we explore the dynamics of the center of mass and the breathing mode in response to time-dependent perturbations of the trap.

arXiv:0707.2937Jul 19, 20070 citations

Recent progress in computational studies of the two-dimensional Hubbard model

Shiwei Zhang

Bulletin of the American Physical SocietyMar 18, 20210 citations

Cluster Gutzwiller method for bosonic lattice systems

Dirk-Sören Lühmann

A versatile and numerically inexpensive method is presented allowing the accurate calculation of phase diagrams for bosonic lattice models. By treating clusters within the Gutzwiller theory, a surprisingly good description of quantum fluctuations beyond the mean-field theory is achieved approaching quantum Monte Carlo predictions for large clusters. Applying this powerful method to the Bose-Hubbard model, we demonstrate that it yields precise results for the superfluid to Mott-insulator transition in square, honeycomb, and cubic lattices. Due to the exact treatment within a cluster, the method can be effortlessly adapted to more complicated Hamiltonians in the fast progressing field of optical lattice experiments. This includes state- and site-dependent superlattices, large confined atomic systems, and disordered potentials, as well as various types of extended Hubbard models. Furthermore, the approach allows an excellent treatment of systems with arbitrary filling factors. We discuss the perspectives that allow for the computation of large, spatially varying lattices, low-lying excitations, and time evolution.A versatile and numerically inexpensive method is presented allowing the accurate calculation of phase diagrams for bosonic lattice models. By treating clusters within the Gutzwiller theory, a surprisingly good description of quantum fluctuations beyond the mean-field theory is achieved approaching quantum Monte Carlo predictions for large clusters. Applying this powerful method to the Bose-Hubbard model, we demonstrate that it yields precise results for the superfluid to Mott-insulator transition in square, honeycomb, and cubic lattices. Due to the exact treatment within a cluster, the method can be effortlessly adapted to more complicated Hamiltonians in the fast progressing field of optical lattice experiments. This includes state- and site-dependent superlattices, large confined atomic systems, and disordered potentials, as well as various types of extended Hubbard models. Furthermore, the approach allows an excellent treatment of systems with arbitrary filling factors. We discuss the perspectives that allow for the computation of large, spatially varying lattices, low-lying excitations, and time evolution.

arXiv:1302.6761Physical Review AApr 12, 201375 citations

Low-lying excitations of

{}^{4}

He and

{}^{3}

He atoms confined inside zeolite cages have been modeled by Bose-Hubbard and Mott-Hubbard rings with strong intrasite repulsion and finite intersite attraction. Differences between

{}^{4}

He and

{}^{3}

He arise due to mass and the statistics. Calculated temperature and concentration dependences of the heat capacity agree qualitatively with the experiment, but a quantitative comparison suggests that disorder may dominate at very low

T