arXiv:cond-mat/9905367

A numerical exact solution of the Bose-Hubbard model

N. Elstner, H. Monien

Published May 25, 1999• 2 citations

Abstract

In this paper we report results from a systematic strong-coupling expansion of the Bose-Hubbard model in one and two spatial dimensions. We obtain numerically exact results for the structure factor and the spectrum of single particle and single hole excitations in the Mott insulator. This enables the determination of the zero-temperature phase diagram and the location of the critical endpoints of the Mott lobes. In one dimension we confirm the occurrence of reentrance behavior from the compressible to the insulating phase in a region close to the critical point.

DOI: 10.48550/arxiv.cond-mat/9905367

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arXiv:cond-mat/9905367

A numerical exact solution of the Bose-Hubbard model

N. Elstner, H. Monien

Published May 25, 1999• 2 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/9905367

Related papers

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We report results from a systematic analytic strong-coupling expansion of the Bose-Hubbard model in one- and two-spatial dimensions. We obtain numerically exact results for the dispersion of single-particle and single-hole excitations in the Mott insulator. The boundary of the Mott phase can be determined with previously unattainable accuracy in one and two dimensions. In one dimension, we observe the occurrence of reentrant behavior from the compressible to the insulating phase in a region close to the critical point, which was conjectured in earlier work. Our calculation can be used as a benchmark for the development of numerical techniques for strongly correlated systems.We report results from a systematic analytic strong-coupling expansion of the Bose-Hubbard model in one- and two-spatial dimensions. We obtain numerically exact results for the dispersion of single-particle and single-hole excitations in the Mott insulator. The boundary of the Mott phase can be determined with previously unattainable accuracy in one and two dimensions. In one dimension, we observe the occurrence of reentrant behavior from the compressible to the insulating phase in a region close to the critical point, which was conjectured in earlier work. Our calculation can be used as a benchmark for the development of numerical techniques for strongly correlated systems.

arXiv:cond-mat/9807033Physical review. B, Condensed matterMay 15, 1999191 citations

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

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arXiv:cond-mat/9508101Physical review. B, Condensed matterFeb 1, 1996353 citations

Monte Carlo study of the two-dimensional Bose-Hubbard model

Barbara Capogrosso-Sansone, Şebnem Güneş Söyler, Nikolay V. Prokof'ev +1 more

One of the most promising applications of ultracold gases in optical lattices is the possibility to use them as quantum emulators of more complex condensed matter systems. We provide benchmark calculations, based on exact quantum Monte Carlo simulations, for the emulator to be tested against. We report results for the ground state phase diagram of the two-dimensional Bose-Hubbard model at unity filling factor. We precisely trace out the critical behavior of the system and resolve the region of small insulating gaps, $\ensuremath{\Delta}⪡J$. The critical point is found to be ${(J/U)}_{c}=0.05974(3)$ , in perfect agreement with the high-order strong-coupling expansion method of Elstner and Monien [Phys. Rev. B 59, 12184 (1999)]. In addition, we present data for the effective mass of particle and hole excitations inside the insulating phase and obtain the critical temperature for the superfluid-normal transition at unity filling factor.One of the most promising applications of ultracold gases in optical lattices is the possibility to use them as quantum emulators of more complex condensed matter systems. We provide benchmark calculations, based on exact quantum Monte Carlo simulations, for the emulator to be tested against. We report results for the ground state phase diagram of the two-dimensional Bose-Hubbard model at unity filling factor. We precisely trace out the critical behavior of the system and resolve the region of small insulating gaps, $\ensuremath{\Delta}⪡J$. The critical point is found to be ${(J/U)}_{c}=0.05974(3)$, in perfect agreement with the high-order strong-coupling expansion method of Elstner and Monien [Phys. Rev. B 59, 12184 (1999)]. In addition, we present data for the effective mass of particle and hole excitations inside the insulating phase and obtain the critical temperature for the superfluid-normal transition at unity filling factor.

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James K. Freericks, H. Monien

The first reliable analytic calculation of the phase diagram of the bose gas on a d-dimensional lattice with on-site repulsion is presented. In one dimension, the analytic calculation is in excellent agreement with the numerical Monte Carlo results. In higher dimensions, the deviations from the Monte Carlo calculations are larger, but the correct shape of the Mott insulator lobes is still obtained. Explicit expressions for the energy of the Mott and the “defect” phase are given in a strong-coupling expansion. Typeset using REVTEX 1 Strongly interacting quantum systems continue to challenge theoretical physics. Fermionic examples of strong correlations include high temperature superconductors, heavy fermion materials and metal-insulator transitions. The study of these systems has been confined to either numerical simulations which are plagued by finite-size effects (with the notable exception of the infinite-dimensional expansion) or uncontrollable approximations. Similar problems arise in strongly interacting bosonic systems which have attracted a lot ofThe first reliable analytic calculation of the phase diagram of the bose gas on a d-dimensional lattice with on-site repulsion is presented. In one dimension, the analytic calculation is in excellent agreement with the numerical Monte Carlo results. In higher dimensions, the deviations from the Monte Carlo calculations are larger, but the correct shape of the Mott insulator lobes is still obtained. Explicit expressions for the energy of the Mott and the “defect” phase are given in a strong-coupling expansion. Typeset using REVTEX 1 Strongly interacting quantum systems continue to challenge theoretical physics. Fermionic examples of strong correlations include high temperature superconductors, heavy fermion materials and metal-insulator transitions. The study of these systems has been confined to either numerical simulations which are plagued by finite-size effects (with the notable exception of the infinite-dimensional expansion) or uncontrollable approximations. Similar problems arise in strongly interacting bosonic systems which have attracted a lot of

Jan 1, 1993100 citations

{(J/U)}_{c}=0.05974(3)

, in perfect agreement with the high-order strong-coupling expansion method of Elstner and Monien [Phys. Rev. B 59, 12184 (1999)]. In addition, we present data for the effective mass of particle and hole excitations inside the insulating phase and obtain the critical temperature for the superfluid-normal transition at unity filling factor.