We study ground-state properties of the one-dimensional truncated (no more than two particles on a site) bosonic Hubbard model in both repulsive and attractive regimes by exact diagonalization and exact world-line Monte Carlo simulation. In the commensurate case (one particle per site) we demonstrate that the point of Mott-insulator--superfluid transition, ${(U/t)}_{c}=0.50\ifmmode\pm\else\textpm\fi{}0.05$, is remarkably far from that of the full model. In the attractive region we observe the phase transition from a one-particle superfluid to a two-particle one. The paring gap demonstrates a linear behavior in the vicinity of the critical point. The critical state features marginal response to the gauge phase. We argue that the two-particle superfluid is a macroscopic analog of a peculiar phase observed earlier in a spin-1 model with axial anisotropy.We study ground-state properties of the one-dimensional truncated (no more than two particles on a site) bosonic Hubbard model in both repulsive and attractive regimes by exact diagonalization and exact world-line Monte Carlo simulation. In the commensurate case (one particle per site) we demonstrate that the point of Mott-insulator--superfluid transition, ${(U/t)}_{c}=0.50\ifmmode\pm\else\textpm\fi{}0.05$, is remarkably far from that of the full model. In the attractive region we observe the phase transition from a one-particle superfluid to a two-particle one. The paring gap demonstrates a linear behavior in the vicinity of the critical point. The critical state features marginal response to the gauge phase. We argue that the two-particle superfluid is a macroscopic analog of a peculiar phase observed earlier in a spin-1 model with axial anisotropy.

arXiv:cond-mat/9709035Physical review. B, Condensed matterJul 15, 199810 citations

Universal conductivity in the two-dimensional boson Hubbard model

G. G. Batrouni, B. E. Larson, Richard T. Scalettar +2 more

We use quantum Monte Carlo methods to evaluate the conductivity \ensuremath{\sigma} of the two-dimensional disordered boson Hubbard model at the superfluid--Bose-glass phase boundary. At the critical point for particle density \ensuremath{\rho}=0.5, we find ${\mathrm{\ensuremath{\sigma}}}_{\mathit{c}}$=(0.45\ifmmode\pm\else\textpm\fi{}0.07)${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$, where ${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$= ${\mathit{e}}_{\mathrm{*}}^{2}$ /h from a finite-size scaling analysis of the superfluid density. We obtain ${\mathrm{\ensuremath{\sigma}}}_{\mathit{c}}$=(0.47\ifmmode\pm\else\textpm\fi{}0.08)${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$ from a direct calculation of the current-current correlation function. Simulations at the critical points for other particle densities, \ensuremath{\rho}=0.75 and 1.0, give similar values for \ensuremath{\sigma}. We discuss possible origins of the difference in this value from that recently obtained by other numerical approaches.We use quantum Monte Carlo methods to evaluate the conductivity \ensuremath{\sigma} of the two-dimensional disordered boson Hubbard model at the superfluid--Bose-glass phase boundary. At the critical point for particle density \ensuremath{\rho}=0.5, we find ${\mathrm{\ensuremath{\sigma}}}_{\mathit{c}}$=(0.45\ifmmode\pm\else\textpm\fi{}0.07)${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$, where ${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=${\mathit{e}}_{\mathrm{*}}^{2}$/h from a finite-size scaling analysis of the superfluid density. We obtain ${\mathrm{\ensuremath{\sigma}}}_{\mathit{c}}$=(0.47\ifmmode\pm\else\textpm\fi{}0.08)${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$ from a direct calculation of the current-current correlation function. Simulations at the critical points for other particle densities, \ensuremath{\rho}=0.75 and 1.0, give similar values for \ensuremath{\sigma}. We discuss possible origins of the difference in this value from that recently obtained by other numerical approaches.

arXiv:cond-mat/9302037Physical review. B, Condensed matterOct 1, 199351 citations

Critical points in the Interacting Boson Model

J. M. Arias

AIP conference proceedingsJan 1, 20041 citation

Exceptional points in the one-dimensional Hubbard model

Rausch Roman, Robert Peters, Tsuneya Yoshida

Jan 1, 20210 citations

Exact diagonalization plus renormalization-group theory: Accurate method for a one-dimensional superfluid-insulator-transition study

V. А. Kashurnikov, Boris V. Svistunov

We use the exact-diagonalization results for a one-dimensional finite-size boson Hubbard-like Hamiltonians to initialize the renormalization-group equations in the vicinity of the superfluid-insulator transition and demonstrate that this provides a rather accurate method of extrapolation of the finite-size results to larger system sizes, and in particular, pinpointing the critical parameters of the Hamiltonians. With our approach we reproduce with the accuracy \ensuremath{\sim}2.5% the known analytical result for the transition point in the half-filled system of hard-core bosons, obtain with a controllable accuracy the critical ratio (t/U ${)}_{\mathit{c}}$ =0.304\ifmmode\pm\else\textpm\fi{}0.002 for the boson Hubbard model, and find out that, in contrast to the general belief, the reduced Hamiltonian (with the constraint that the site occupation numbers be less than 3) is far from being a good approximation to the full model. \textcopyright{} 1996 The American Physical Society.We use the exact-diagonalization results for a one-dimensional finite-size boson Hubbard-like Hamiltonians to initialize the renormalization-group equations in the vicinity of the superfluid-insulator transition and demonstrate that this provides a rather accurate method of extrapolation of the finite-size results to larger system sizes, and in particular, pinpointing the critical parameters of the Hamiltonians. With our approach we reproduce with the accuracy \ensuremath{\sim}2.5% the known analytical result for the transition point in the half-filled system of hard-core bosons, obtain with a controllable accuracy the critical ratio (t/U${)}_{\mathit{c}}$=0.304\ifmmode\pm\else\textpm\fi{}0.002 for the boson Hubbard model, and find out that, in contrast to the general belief, the reduced Hamiltonian (with the constraint that the site occupation numbers be less than 3) is far from being a good approximation to the full model. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterMay 1, 199656 citations

{\mathit{e}}_{\mathrm{*}}^{2}

/h from a finite-size scaling analysis of the superfluid density. We obtain ${\mathrm{\ensuremath{\sigma}}}_{\mathit{c}}$=(0.47\ifmmode\pm\else\textpm\fi{}0.08)${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$ from a direct calculation of the current-current correlation function. Simulations at the critical points for other particle densities, \ensuremath{\rho}=0.75 and 1.0, give similar values for \ensuremath{\sigma}. We discuss possible origins of the difference in this value from that recently obtained by other numerical approaches.

{)}_{\mathit{c}}

=0.304\ifmmode\pm\else\textpm\fi{}0.002 for the boson Hubbard model, and find out that, in contrast to the general belief, the reduced Hamiltonian (with the constraint that the site occupation numbers be less than 3) is far from being a good approximation to the full model. \textcopyright{} 1996 The American Physical Society.