Using the x-y model and a nonlocal updating scheme called cluster Monte Carlo, we calculate the superfluid density of a two-dimensional superfluid on large-size square lattices L\ifmmode\times\else\texttimes\fi{}L up to 400\ifmmode\times\else\texttimes\fi{}400. This technique allows us to approach temperatures close to the critical point, and by studying a wide range of L values and applying finite-size scaling theory we are able to extract the critical properties of the system. We calculate the superfluid density and from that we extract the renormalization-group beta function. We derive finite-size scaling expressions using the Kosterlitz-Thouless-Nelson renormalization group equations and show that they are in very good agreement with our numerical results. This allows us to extrapolate our results to the infinite-size limit. We also find that the universal discontinuity of the superfluid density at the critical temperature is in very good agreement with the Kosterlitz-Thouless-Nelson calculation and experiments.Using the x-y model and a nonlocal updating scheme called cluster Monte Carlo, we calculate the superfluid density of a two-dimensional superfluid on large-size square lattices L\ifmmode\times\else\texttimes\fi{}L up to 400\ifmmode\times\else\texttimes\fi{}400. This technique allows us to approach temperatures close to the critical point, and by studying a wide range of L values and applying finite-size scaling theory we are able to extract the critical properties of the system. We calculate the superfluid density and from that we extract the renormalization-group beta function. We derive finite-size scaling expressions using the Kosterlitz-Thouless-Nelson renormalization group equations and show that they are in very good agreement with our numerical results. This allows us to extrapolate our results to the infinite-size limit. We also find that the universal discontinuity of the superfluid density at the critical temperature is in very good agreement with the Kosterlitz-Thouless-Nelson calculation and experiments.

arXiv:cond-mat/9310034Physical review. B, Condensed matterMay 1, 199455 citations

A quantum mechanical determination of the superfluid density

H. Haug, K. Weiss

The European Physical Journal BAug 1, 19722 citations

SCALING LAW OF SUPERFLUID–INSULATOR TRANSITION IN THE 1D BOSE–HUBBARD MODEL

Shi-Jian Gu, Junpeng Cao, Shu Chen +1 more

The finite size scaling behavior of superfluid–insulator transition in the one-dimensional Bose–Hubbard model is studied. It is shown that the superfluid density of the system with finite size has a maximum at a certain interaction Um and the derivative of superfluid density has a minimum at a certain interaction Ud. The critical point Uc can be quantified by the scaling analysis of either Um or Ud. The transition point Um tends to the critical point Uc from the region of U < Uc, while the Ud tends to the Uc from the region of U > Uc. The transition points Um and Ud satisfy different finite size scaling laws and have the different critical exponents. The divergence speed of the superfluid density is much smaller than that of its derivative at the critical point.The finite size scaling behavior of superfluid–insulator transition in the one-dimensional Bose–Hubbard model is studied. It is shown that the superfluid density of the system with finite size has a maximum at a certain interaction Um and the derivative of superfluid density has a minimum at a certain interaction Ud. The critical point Uc can be quantified by the scaling analysis of either Um or Ud. The transition point Um tends to the critical point Uc from the region of U < Uc, while the Ud tends to the Uc from the region of U > Uc. The transition points Um and Ud satisfy different finite size scaling laws and have the different critical exponents. The divergence speed of the superfluid density is much smaller than that of its derivative at the critical point.

International Journal of Modern Physics BFeb 2, 20123 citations

Superfluid density of the two-dimensional strong-coupling attractive Hubbard model

Jürgen Stein

Physics Letters AJan 1, 19971 citation

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

{\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.