Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

Bose-Hubbard model with local two- and three-body interaction under off-diagonal confinement

Greis J. Cruz, R Franco, Jereson Silva-Valencia

Published Apr 1, 2014• 1 citation
Publisher

Abstract

We calculate the density profiles of a system of bosons with off-diagonal confinement and local interaction between two or three particles, using the density matrix renormalizaction group method. We found different ground-states: Mott insulator, superfluid and diverse mixed states. We observe that the Mott insulator lobes are surrounded by Mott insulator-superfluid coexistence state regardless the kind of the local interaction. The area of the Mott insulator lobes decreases for the two-body interactions and remain the same for three-body interactions.

DOI
10.1088/1742-6596/480/1/012003

Related papers

One-dimensional Bose-Hubbard model with local three-body interactions

Satoshi Ejima, Florian Lange, Holger Fehske +2 more

We employ the (dynamical) density-matrix renormalization-group technique to investigate the ground-state properties of the Bose-Hubbard model with nearest-neighbor transfer amplitudes $t$ and local two-body and three-body repulsion of strength $U$ and $W$, respectively. We determine the phase boundaries between the Mott-insulating and superfluid phases for the lowest two Mott lobes from the chemical potentials. We calculate the tips of the Mott lobes from the Tomonaga-Luttinger liquid parameter and confirm the positions of the Kosterlitz-Thouless points from the von Neumann entanglement entropy. We find that physical quantities in the second Mott lobe such as the gap and the dynamical structure factor scale almost perfectly in $t/(U+W)$, even close to the Mott transition. Strong-coupling perturbation theory shows that there is no true scaling but deviations from it are quantitatively small in the strong-coupling limit. This observation should remain true in higher dimensions and for not too large attractive three-body interactions.

arXiv:1310.4719•Physical Review A•Dec 12, 2013•14 citations

Mott lobes of the S=1 Bose-Hubbard model with three-body interactions

A. F. Hincapie-F, R. Franco, Jereson Silva-Valencia

Using the density-matrix renormalization-group method, we studied the ground state of the one-dimensional $S=1$ Bose-Hubbard model with local three-body interactions, which can be a superfluid or a Mott insulator state. We drew the phase diagram of this model for both ferromagnetic and antiferromagnetic interaction. Regardless of the sign of the spin-dependent coupling, we obtained that the Mott lobes area decreases as the spin-dependent strength increases, which means that the even-odd asymmetry of the two-body antiferromagnetic chain is absent for local three-body interactions. For antiferromagnetic coupling, we found that the density drives first-order superfluid-Mott insulator transitions for even and odd lobes. Ferromagnetic Mott insulator and superfluid states were obtained with a ferromagnetic coupling, and a tendency to a ``long-range'' order was observed.

arXiv:1607.02302•Physical Review A•Sep 19, 2016•11 citations

Two-body repulsive bound pairs in a multibody interacting Bose-Hubbard model

Suman Mondal, Augustine Kshetrimayum, Tapan Mishra

We study the system of multibody interacting bosons on a two-dimensional optical lattice and analyze the formation of bound bosonic pairs in the context of the Bose-Hubbard model. Assuming a repulsive two-body interaction we obtain the signatures of pair formation in the regions between the Mott insulator lobes of the phase diagram for different choices of higher-order local interactions. Considering the most general Bose-Hubbard model involving local multibody interactions we investigate the ground state properties utilizing the cluster mean-field theory approach and further confirm the results by means of sophisticated infinite projected entangled pair states calculations. By using various order parameters, we show that the choice of higher-order interaction can lead to pair superfluid phase in the system between two different Mott lobes. We also analyze the effect of temperature and density-dependent tunneling to establish the stability of the PSF phase.

arXiv:2002.11317•Physical Review A•Aug 13, 2020•22 citations

First Mott lobe of bosons with local two- and three-body interactions

Jereson Silva-Valencia, André M. C. Souza

Using the density matrix renormalization group method, we determine the phase diagram of the Bose-Hubbard model with local two- and three-body interactions, describing polar molecules in one-dimensional optical lattices. The difference in the block von Neumann entropy with different system sizes was used to establish the critical points. We found that the quantum critical point position increases with the three-body interaction. We show that the model studied is in the same universality class as the model with pure two-body interactions.

Physical Review A•Dec 6, 2011•35 citations

One-dimensional Bose-Hubbard model with pure three-body interactions

Tomasz Sowiński

Abstract The extended Bose-Hubbard model with pure three-body local interactions is studied using the Density Matrix Renormalization Group approach. The shapes of the first two insulating lobes are discussed, and the values of the critical tunneling for which the system undergoes the quantum phase transition from insulating to superfluid phase are predicted. It is shown that stability of insulating phases, in contrast to the standard Bose-Hubbard model, is enhanced for larger fillings. It is also shown that, on the tip of the boundary of the insulating phase, the model under consideration belongs to the Berenzinskii-Kosterlitz-Thouless universality class.

arXiv:1307.6852•Open Physics•Jan 1, 2014•12 citations

Dynamic properties of the one-dimensional Bose-Hubbard model

Satoshi Ejima, Holger Fehske, Florian Gebhard

We use the density-matrix renormalization group method to investigate ground-state and dynamic properties of the one-dimensional Bose-Hubbard model, the effective model of ultracold bosonic atoms in an optical lattice. For fixed maximum site occupancy n b = 5, we calculate the phase boundaries between the Mott insulator and the "superfluid" phase for the lowest two Mott lobes. We extract the Tomonaga-Luttinger parameter from the density-density correlation function and determine accurately the critical interaction strength for the Mott transition. For both phases, we study the momentum distribution function in the homogeneous system, and the particle distribution and quasi-momentum distribution functions in a parabolic trap. With our zero-temperature method we determine the photoemission spectra in the Mott insulator and in the "superfluid" phase of the one-dimensional Bose-Hubbard model. In the insulator, the Mott gap separates the quasi-particle and quasi-hole dispersions. In the "superfluid" phase the spectral weight is concentrated around zero momentum.

arXiv:1102.2028•Europhysics Letters (EPL)•Feb 1, 2011•105 citations
We calculate the density profiles of a system of bosons with off-diagonal confinement and local interaction between two or three particles, using the density matrix renormalizaction group method. We found different ground-states: Mott insulator, superfluid and diverse mixed states. We observe that the Mott insulator lobes are surrounded by Mott insulator-superfluid coexistence state regardless the kind of the local interaction. The area of the Mott insulator lobes decreases for the two-body interactions and remain the same for three-body interactions.
We employ the (dynamical) density-matrix renormalization-group technique to investigate the ground-state properties of the Bose-Hubbard model with nearest-neighbor transfer amplitudes ttt and local two-body and three-body repulsion of strength UUU and WWW, respectively. We determine the phase boundaries between the Mott-insulating and superfluid phases for the lowest two Mott lobes from the chemical potentials. We calculate the tips of the Mott lobes from the Tomonaga-Luttinger liquid parameter and confirm the positions of the Kosterlitz-Thouless points from the von Neumann entanglement entropy. We find that physical quantities in the second Mott lobe such as the gap and the dynamical structure factor scale almost perfectly in t/(U+W)t/(U+W)t/(U+W), even close to the Mott transition. Strong-coupling perturbation theory shows that there is no true scaling but deviations from it are quantitatively small in the strong-coupling limit. This observation should remain true in higher dimensions and for not too large attractive three-body interactions.
Using the density-matrix renormalization-group method, we studied the ground state of the one-dimensional S=1S=1S=1 Bose-Hubbard model with local three-body interactions, which can be a superfluid or a Mott insulator state. We drew the phase diagram of this model for both ferromagnetic and antiferromagnetic interaction. Regardless of the sign of the spin-dependent coupling, we obtained that the Mott lobes area decreases as the spin-dependent strength increases, which means that the even-odd asymmetry of the two-body antiferromagnetic chain is absent for local three-body interactions. For antiferromagnetic coupling, we found that the density drives first-order superfluid-Mott insulator transitions for even and odd lobes. Ferromagnetic Mott insulator and superfluid states were obtained with a ferromagnetic coupling, and a tendency to a ``long-range'' order was observed.
We study the system of multibody interacting bosons on a two-dimensional optical lattice and analyze the formation of bound bosonic pairs in the context of the Bose-Hubbard model. Assuming a repulsive two-body interaction we obtain the signatures of pair formation in the regions between the Mott insulator lobes of the phase diagram for different choices of higher-order local interactions. Considering the most general Bose-Hubbard model involving local multibody interactions we investigate the ground state properties utilizing the cluster mean-field theory approach and further confirm the results by means of sophisticated infinite projected entangled pair states calculations. By using various order parameters, we show that the choice of higher-order interaction can lead to pair superfluid phase in the system between two different Mott lobes. We also analyze the effect of temperature and density-dependent tunneling to establish the stability of the PSF phase.
Using the density matrix renormalization group method, we determine the phase diagram of the Bose-Hubbard model with local two- and three-body interactions, describing polar molecules in one-dimensional optical lattices. The difference in the block von Neumann entropy with different system sizes was used to establish the critical points. We found that the quantum critical point position increases with the three-body interaction. We show that the model studied is in the same universality class as the model with pure two-body interactions.
Abstract The extended Bose-Hubbard model with pure three-body local interactions is studied using the Density Matrix Renormalization Group approach. The shapes of the first two insulating lobes are discussed, and the values of the critical tunneling for which the system undergoes the quantum phase transition from insulating to superfluid phase are predicted. It is shown that stability of insulating phases, in contrast to the standard Bose-Hubbard model, is enhanced for larger fillings. It is also shown that, on the tip of the boundary of the insulating phase, the model under consideration belongs to the Berenzinskii-Kosterlitz-Thouless universality class.
We use the density-matrix renormalization group method to investigate ground-state and dynamic properties of the one-dimensional Bose-Hubbard model, the effective model of ultracold bosonic atoms in an optical lattice. For fixed maximum site occupancy n b = 5, we calculate the phase boundaries between the Mott insulator and the "superfluid" phase for the lowest two Mott lobes. We extract the Tomonaga-Luttinger parameter from the density-density correlation function and determine accurately the critical interaction strength for the Mott transition. For both phases, we study the momentum distribution function in the homogeneous system, and the particle distribution and quasi-momentum distribution functions in a parabolic trap. With our zero-temperature method we determine the photoemission spectra in the Mott insulator and in the "superfluid" phase of the one-dimensional Bose-Hubbard model. In the insulator, the Mott gap separates the quasi-particle and quasi-hole dispersions. In the "superfluid" phase the spectral weight is concentrated around zero momentum.