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arXiv:1311.1954 · Physical Review A

Numerical studies of ground-state fidelity of the Bose-Hubbard model

Mateusz Łącki, Bogdan Damski, Jakub Zakrzewski

Published Mar 20, 2014• 24 citations
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Abstract

We compute ground-state fidelity of the one-dimensional Bose-Hubbard model at unit filling factor. To this aim, we apply the density matrix renormalization group algorithm to systems with open and periodic boundary conditions. We find that fidelity differs significantly in the two cases and study its scaling properties in the quantum critical regime.

DOI
10.1103/physreva.89.033625

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We compute ground-state fidelity of the one-dimensional Bose-Hubbard model at unit filling factor. To this aim, we apply the density matrix renormalization group algorithm to systems with open and periodic boundary conditions. We find that fidelity differs significantly in the two cases and study its scaling properties in the quantum critical regime.
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We study the effect of different open boundary conditions on the insulating ground states of the one-dimensional extended Bose-Hubbard model at and near unit filling. To this end, we employ the density-matrix renormalization-group method with system sizes up to 250 sites. To characterize the system, various order parameters and entanglement entropies are calculated. When opposite edge potentials are added to the two ends of the chain, the inversion symmetry is explicitly broken, and the regular bulk phases appear. On the other hand, simple open boundary conditions often exhibit nondegenerate ground states with a domain wall in the middle of the chain, which induces a sign flip of an order parameter. Such a domain wall can lead to an algebraic behavior of the off diagonals of the single-particle density matrix. We show that this algebraic behavior adds only a finite contribution to the entanglement entropy, which does not diverge as the system size increases. Therefore, it is not an indication of a superfluid phase. We confirm this picture by analytical calculations based on an effective Hamiltonian for a domain wall.
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We revisit the one-dimensional attractive Hubbard model by using the Bethe-ansatz-based density-functional theory and density-matrix renormalization method. The ground-state properties of this model are discussed in details for different fillings and different confining conditions in weak-to-intermediate coupling regime. We investigate the ground-state energy, energy gap, and pair-binding energy and compare them with those calculated from the canonical Bardeen-Cooper-Schrieffer approximation. We find that the Bethe-ansatz-based density-functional theory is computationally easy and yields an accurate description of the ground-state properties for weak-to-intermediate interaction strength, different fillings, and confinements. In order to characterize the quantum phase transition in the presence of a harmonic confinement, we calculate the thermodynamic stiffness, the density-functional fidelity, and fidelity susceptibility, respectively. It is shown that with the increase in the number of particles or attractive interaction strength, the system can be driven from the Luther-Emery-type phase to the composite phase of Luther-Emery-type in the wings and insulatinglike in the center.
We study the ground state quantum phase transition by means of entanglement in the one-dimensional asymmetric Hubbard model with open boundary conditions. The local entanglement between the middle two sites and the rest of the system, and the block entanglement between the left and right portions of the system, are calculated using the density-matrix renormalization group (DMRG) method. We find that the entanglement shows interesting scaling and singular behavior around the phase transition line.