arXiv:cond-mat/0701739 · AIP conference proceedings

Accurate determination of the superfluid-insulator transition in the one-dimensional Bose-Hubbard model

Jakub Zakrzewski, Dominique Delande, Marko Robnik, Valery G. Romanovski

Published Jan 1, 2008• 18 citations

Abstract

The quantum phase transition point between the insulator and the superfluid phase at unit filling factor of the infinite one‐dimensional Bose‐Hubbard model is numerically computed with a high accuracy. The method uses the infinite system version of the time evolving block decimation algorithm, here tested in a challenging case. We provide also the accurate estimate of the phase transition point at double occupancy.

DOI: 10.1063/1.3046265

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arXiv:cond-mat/0701739 · AIP conference proceedings

Accurate determination of the superfluid-insulator transition in the one-dimensional Bose-Hubbard model

Jakub Zakrzewski, Dominique Delande, Marko Robnik, Valery G. Romanovski

Published Jan 1, 2008• 18 citations

arXiv HTML PDF

Abstract

DOI: 10.1063/1.3046265

Related papers

Superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model for arbitrary integer filling factors

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n=1

is found to be at

{(U∕t)}_{\mathrm{c}}=29.34(2)

, and the insulating gap $\ensuremath{\Delta}$ is measured with accuracy of a few percent of the hopping amplitude

t

. We obtain the effective mass of particle and hole excitations in the insulating state---with explicit demonstration of the emerging particle-hole symmetry and relativistic dispersion law at the transition tip---along with the sound velocity in the strongly correlated superfluid phase. These parameters are the necessary ingredients to perform analytic estimates of the low temperature $(T⪡\ensuremath{\Delta})$ thermodynamics in macroscopic samples. We present accurate thermodynamic curves, including these for specific heat and entropy, for typical insulating

(U∕t=40)

and superfluid

(t∕U=0.0385)

phases. Our data can serve as a basis for accurate experimental thermometry, and a guide for appropriate initial conditions if one attempts to use interacting bosons in quantum information processing.

d>3

and to the quantum rotor limit of high filling, which refers to an array of Josephson junctions.

We investigate the interaction-induced superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings

n=1

n=2

, and

n=3

by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.