Physical Review Letters

One-Dimensional Disordered Bosonic Hubbard Model: A Density-Matrix Renormalization Group Study

Ramesh V. Pai, Rahul Anil Pandit, H. R. Krishnamurthy, S. Ramasesha

Published Apr 15, 1996• 108 citations

Abstract

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.

DOI: 10.1103/physrevlett.76.2937

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Physical Review Letters

One-Dimensional Disordered Bosonic Hubbard Model: A Density-Matrix Renormalization Group Study

Ramesh V. Pai, Rahul Anil Pandit, H. R. Krishnamurthy, S. Ramasesha

Published Apr 15, 1996• 108 citations

Publisher

Abstract

\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.

DOI: 10.1103/physrevlett.76.2937

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We use the density matrix renormalization group to study the quantum transitions that occur in the half-filled one-dimensional fermionic Hubbard model with onsite potential disorder. We find a transition from the gapped Mott phase with algebraic spin correlations to a gapless spin-disordered phase beyond a critical strength of the disorder $Δ_c \approx U/2$ . Both the transitions in the charge and spin sectors are shown to be coincident. We also establish the finite-size corrections to the charge gap and the spin-spin correlation length in the presence of disorder and using a finite-size-scaling analysis we obtain the zero temperature phase diagram of the various quantum phase transitions that occur in the disorder-interaction plane.We use the density matrix renormalization group to study the quantum transitions that occur in the half-filled one-dimensional fermionic Hubbard model with onsite potential disorder. We find a transition from the gapped Mott phase with algebraic spin correlations to a gapless spin-disordered phase beyond a critical strength of the disorder $Δ_c \approx U/2$. Both the transitions in the charge and spin sectors are shown to be coincident. We also establish the finite-size corrections to the charge gap and the spin-spin correlation length in the presence of disorder and using a finite-size-scaling analysis we obtain the zero temperature phase diagram of the various quantum phase transitions that occur in the disorder-interaction plane.

arXiv:cond-mat/9704027Apr 3, 19971 citation

\ensuremath{\beta}

We use the finite-size, density-matrix-renormalization-group (FSDMRG) method to obtain the phase diagram of the one-dimensional

(d=1)

extended Bose-Hubbard model for density $\ensuremath{\rho}=1$ in the $U\ensuremath{-}V$ plane, where

U

and

V

are, respectively, onsite and nearest-neighbor interactions. The phase diagram comprises three phases: superfluid (SF), Mott insulator (MI), and mass-density-wave (MDW). For small values of

U

and

V

, we get a reentrant SF-MI-SF phase transition. For intermediate values of interactions the SF phase is sandwiched between MI and MDW phases with continuous SF-MI and SF-MDW transitions. We show, by a detailed, finite-size scaling analysis, that the MI-SF transition is of Kosterlitz-Thouless (KT) type whereas the MDW-SF transition has both KT and two-dimensional Ising characters. For large values of

U

and

V

we get a direct, first-order, MI-MDW transition. The MI-SF, MDW-SF, and MI-MDW phase boundaries join at a bicritical point at $(U,V)=(8.5\ifmmode\pm\else\textpm\fi{}0.05,4.75\ifmmode\pm\else\textpm\fi{}0.05)$.

Δ_c \approx U/2

. Both the transitions in the charge and spin sectors are shown to be coincident. We also establish the finite-size corrections to the charge gap and the spin-spin correlation length in the presence of disorder and using a finite-size-scaling analysis we obtain the zero temperature phase diagram of the various quantum phase transitions that occur in the disorder-interaction plane.