We use the density-matrix renormalization group to study the one-dimensional bosonic Hubbard model, with and without disorder. We obtain the gaps in all phases, certain correlation functions, and the superfluid density. A finite-size-scaling analysis enables us to obtain an accurate phase diagram and the $\ensuremath{\beta}$ function at the superfluid--Mott insulator transition and the Kosterlitz-Thouless essential singularity in the pure case. We also obtain coupling constants used in effective field theories for this system.We use the density-matrix renormalization group to study the one-dimensional bosonic Hubbard model, with and without disorder. We obtain the gaps in all phases, certain correlation functions, and the superfluid density. A finite-size-scaling analysis enables us to obtain an accurate phase diagram and the $\ensuremath{\beta}$ function at the superfluid--Mott insulator transition and the Kosterlitz-Thouless essential singularity in the pure case. We also obtain coupling constants used in effective field theories for this system.

Physical Review LettersApr 15, 1996108 citations

Superfluid density of two-dimensional weakly interacting boson system at zero temperature

Pei-Song He, Yuwei Fan

Chinese Science BulletinApr 1, 20110 citations

Superfluid Density in Pairing Theory of Superfluidity

W. A. B. EVANS, R. I. M. A. Rashid

Springer eBooksJan 1, 19741 citation

RENORMALIZED BOSONS AND FERMIONS

Klaus A. Gernoth, MANFRED L. RISTIG

Correlated Density Matrix (CDM) theory permits formal analyses of microscopic properties of strongly correlated quantum fluids and liquids at nonzero temperatures. Equilibrium properties, thermodynamic potentials, correlation and structure functions can be studied formally as well as numerically within the CDM algorithm. Here we provide the essential building blocks for studying the radial distribution function and the single-particle momentum distribution of the ingredients of the quantum systems. We focus on the statistical properties of correlated fluids and introduce the concept of renormalized bosons and fermions. These entities carry the main statistical features of the correlated systems such as liquid 4 He through their specific dependence on temperature, particle number density, and wavenumber encapsulated in their effective masses. The formalism is developed for systems of bosons and of fermions. Numerical calculations for fluid 4 He in the normal phase demonstrate the power of the renormalization concept. The formalism is further extended to analyze the Bose-Einstein condensed phases and gives a microscopic understanding of Tisza's two-fluid model for the normal and superfluid density components.Correlated Density Matrix (CDM) theory permits formal analyses of microscopic properties of strongly correlated quantum fluids and liquids at nonzero temperatures. Equilibrium properties, thermodynamic potentials, correlation and structure functions can be studied formally as well as numerically within the CDM algorithm. Here we provide the essential building blocks for studying the radial distribution function and the single-particle momentum distribution of the ingredients of the quantum systems. We focus on the statistical properties of correlated fluids and introduce the concept of renormalized bosons and fermions. These entities carry the main statistical features of the correlated systems such as liquid 4 He through their specific dependence on temperature, particle number density, and wavenumber encapsulated in their effective masses. The formalism is developed for systems of bosons and of fermions. Numerical calculations for fluid 4 He in the normal phase demonstrate the power of the renormalization concept. The formalism is further extended to analyze the Bose-Einstein condensed phases and gives a microscopic understanding of Tisza's two-fluid model for the normal and superfluid density components.

International Journal of Modern Physics BOct 20, 20102 citations

Spatial correlations of trapped one-dimensional bosons in an optical lattice

Corinna Kollath, Ulrich Schollwöck, Jan von Delft +1 more

We investigate a quasi-one-dimensional system of trapped cold bosonic atoms in an optical lattice by using the density-matrix renormalization group to study the Bose-Hubbard model at $T=0$ for experimentally realistic numbers of lattice sites. It is shown that a properly rescaled one-particle density matrix characterizes superfluid versus insulating states just as in the homogeneous system. For typical parabolic traps we also confirm the widely used local-density approach for describing correlations in the limit of weak interaction. Finally, we note that the superfluid to Mott-insulating transition is seen most directly in the half-width of the interference peak.We investigate a quasi-one-dimensional system of trapped cold bosonic atoms in an optical lattice by using the density-matrix renormalization group to study the Bose-Hubbard model at $T=0$ for experimentally realistic numbers of lattice sites. It is shown that a properly rescaled one-particle density matrix characterizes superfluid versus insulating states just as in the homogeneous system. For typical parabolic traps we also confirm the widely used local-density approach for describing correlations in the limit of weak interaction. Finally, we note that the superfluid to Mott-insulating transition is seen most directly in the half-width of the interference peak.

arXiv:cond-mat/0310388Physical Review AMar 9, 2004118 citations

We investigate a quasi-one-dimensional system of trapped cold bosonic atoms in an optical lattice by using the density-matrix renormalization group to study the Bose-Hubbard model at

T=0

for experimentally realistic numbers of lattice sites. It is shown that a properly rescaled one-particle density matrix characterizes superfluid versus insulating states just as in the homogeneous system. For typical parabolic traps we also confirm the widely used local-density approach for describing correlations in the limit of weak interaction. Finally, we note that the superfluid to Mott-insulating transition is seen most directly in the half-width of the interference peak.