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

arXiv:1705.00475 · Annalen der Physik

Spin‐1 Bose Hubbard Model with Nearest Neighbour Extended Interaction

Sk Noor Nabi, Saurabh Basu

Published Oct 24, 2017• 5 citations
arXivHTMLPDF

Abstract

Abstract A spinor ( ) Bose gas is studied in presence of a density‐density interaction through a mean field approach and a perturbation theory for either sign of the spin dependent interaction, namely the antiferromagnetic (AF) and the ferromagnetic cases. In the AF case, the charge density wave (CDW) phase appears to be sandwiched between the Mott insulating (MI) and the supersolid phases for small values of the extended interaction strength. But the CDW phase completely occupies the MI lobe when the extended interaction strength is larger than a certain critical value related to the width of the MI lobes and hence opens up the possibilities of spin singlet and nematic CDW insulating phases. In the ferromagnetic case, the phase diagram shows similar features as that of the AF case and are in complete agreement with a spin‐0 Bose gas. The perturbation expansion calculations nicely corroborate the mean field phase results in both these cases. Further, we extend our calculations in presence of a harmonic confinement and obtained the momentum distribution profile that is related to the absorption spectra in order to distinguish between different phases.

DOI
10.1002/andp.201700245

Related papers

Interplay of the Staggered and Three‐Body Interaction Potentials on the Quantum Phases of a Spin‐1 Ultracold Atom in an Optical Lattice

Sk Noor Nabi

Abstract The interplay of the staggered and the three‐body interaction potentials on the quantum phases of a spin‐1 Bose Hubbard model using a mean field approximation (MFA) is studied. In the antiferromagnetic (AF) case, a smaller value of the staggered potential (SP) results in the charge and the spin density wave ordering along with the Mott insulator (MI) and the staggered superfluid (SSF) phases. While the competition between two types of the potential leads to the stabilization of the higher order MI and charge density wave (CDW) phases with increasing three‐body interaction strength. Further, the spin eigenvalue and nematic order parameters are calculated to scrutinize the spin singlet‐nematic formation in the MI and the CDW phases and spin population fractions to analyze the nature of the SSF phase. A signature of the spin density wave (SDW) pattern is also observed in the gapped phase lobes. In case of a purely three‐body interaction, the third and higher order insulating lobes become dominant with increasing staggered potential strength. Subsequently, all MFA phase diagrams are then nicely corroborated with the analytical results obtained using a perturbative expansion corresponding to the AF and ferromagnetic cases.

Annalen der Physik•Dec 22, 2022•1 citation

Disorder, three body interaction and Bose glass phase in a spinor atomic gas in an optical lattice

Sk Noor Nabi, Saurabh Basu

We study the effects of disorder on the spin dependent interaction term of a spinor Bose Hubbard model with a three body interaction potential. The signature of the Bose glass (BG) phase is observed by computing the fraction of the lattice sites having finite superfluid (SF) order parameter and non integer occupation densities. We obtain the phase diagram both for the antiferromagnetic (AF) and ferromagnetic (F) cases via a percolation analysis. In the AF case, the BG phase intervenes between the odd-even Mott insulating (MI) lobes (for example, the lobes corresponding to occupation densities, n=1 and (n=2) but not between the even-odd MI lobes. In the ferromagnetic case, the presence of the BG phase is observed between all the MI lobes irrespective of them being even or odd. The BG phase almost destroys the first MI lobe while the MI phase looks more stable than the SF phase both in the AF and F cases due to the presence of the three body interactions.

Journal of Physics Conference Series•Oct 1, 2016•0 citations

Effects of an attractive three-body interaction on a spin-1 Bose Hubbard model

Sk Noor Nabi, Saurabh Basu

Abstract We study the effects of an attractive three-body interaction potential on a spin-1 ultracold Bose gas using the mean field approach (MFA). For an antiferromagnetic interaction, the third Mott insulator (MI) lobe is predominantly affected, where it completely engulfs the second and the fourth MI lobes at large values of interaction strength. However, no significant change is observed beyond the fourth MI lobe. The formation of the spin singlet (nematic) MI phase and the different order of phase transitions to the superfluid phase have been carefully scrutinized with the help of spin eigenvalues and the spin nematic order parameter. In the ferromagnetic case, the phase diagram shows similar features to that of a scalar Bose gas. We have compared our results on the MFA phase diagrams for both types of interaction potential via a perturbation expansion in both cases.

arXiv:1806.11450•Laser Physics•May 28, 2019•0 citations

Cluster mean field theory for two-dimensional spin-1 Bose–Hubbard model

Bhargav K. Alavani, Ananya Das, Ramesh V. Pai

Abstract Cluster mean field theory for the two-dimensional spin-1 Bose–Hubbard model is applied to study superfluid (SF) to Mott insulator (MI) phase transitions and various magnetic phases that arise in the presence of spin-dependent anti-ferromagnetic and ferromagnetic interactions. This study clearly shows the nematic behavior of SF and odd-density MI phases, and a continuous phase transition between them for anti-ferromagnetic interaction. The even-density MI shows a nematic or singlet phase depending upon the strength of the interaction, and a continuous crossover between them. The SF to singlet MI transition is discontinuous. The dependence of cluster size on the critical on-site interaction ( U 0 C ) for SF to MI transitions is also studied. In the case of anti-ferromagnetic interaction, it is found that U 0 C for the SF to odd-density MI transition decreases with cluster size; however, no such changes are observed for the SF to singlet MI transition. In the case of ferromagnetic interactions, SF to MI transitions are continuous, and Mott lobes become enlarged with cluster size. Second order Rényi entanglement entropy (EE) is calculated in different phases. The results show that Rényi EE is large in the nematic MI phase.

Journal of Physics B Atomic Molecular and Optical Physics•May 17, 2018•12 citations

Disordered spinor Bose-Hubbard model

Mateusz Łącki, Simone Paganelli, V. Ahufinger +2 more

We study the zero-temperature phase diagram of the disordered spin-$1$ Bose-Hubbard model in a two-dimensional square lattice. To this aim, we use a mean-field Gutzwiller ansatz and a probabilistic mean-field perturbation theory. The spin interaction induces two different regimes, corresponding to a ferromagnetic and antiferromagnetic order. In the ferromagnetic case, the introduction of disorder reproduces analogous features of the disordered scalar Bose-Hubbard model, consisting in the formation of a Bose glass phase between Mott insulator lobes. In the antiferromagnetic regime, the phase diagram differs more from the scalar case. Disorder in the chemical potential can lead to the disappearance of Mott insulator lobes with an odd-integer filling factor and, for sufficiently strong spin coupling, to Bose glass of singlets between even-filling Mott insulator lobes. Disorder in the spinor coupling parameter results in the appearance of a Bose glass phase only between the $n$ and the $n+1$ lobes for $n$ odd. Disorder in the scalar Hubbard interaction inhibits Mott insulator regions for occupation larger than a critical value.

arXiv:1007.5177•Physical Review A•Jan 14, 2011•27 citations

The inhomogeneous extended Bose‐Hubbard model: A mean‐field theory

Jamshid Moradi Kurdestany, R.V. Pai, Rahul Anil Pandit

Abstract We develop an inhomogeneous mean‐field theory for the extended Bose‐Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean‐field theory yields the phase diagram of the homogeneous extended Bose‐Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott‐insulator (MI), density‐wave (DW), and supersolid (SS) phases in the plane of the chemical potential µ and on‐site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest‐neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density‐wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold‐atom dipolar condensates in optical lattices in a confining potential.

arXiv:1201.6451•Annalen der Physik•Feb 2, 2012•20 citations
Abstract A spinor ( ) Bose gas is studied in presence of a density‐density interaction through a mean field approach and a perturbation theory for either sign of the spin dependent interaction, namely the antiferromagnetic (AF) and the ferromagnetic cases. In the AF case, the charge density wave (CDW) phase appears to be sandwiched between the Mott insulating (MI) and the supersolid phases for small values of the extended interaction strength. But the CDW phase completely occupies the MI lobe when the extended interaction strength is larger than a certain critical value related to the width of the MI lobes and hence opens up the possibilities of spin singlet and nematic CDW insulating phases. In the ferromagnetic case, the phase diagram shows similar features as that of the AF case and are in complete agreement with a spin‐0 Bose gas. The perturbation expansion calculations nicely corroborate the mean field phase results in both these cases. Further, we extend our calculations in presence of a harmonic confinement and obtained the momentum distribution profile that is related to the absorption spectra in order to distinguish between different phases.
Abstract The interplay of the staggered and the three‐body interaction potentials on the quantum phases of a spin‐1 Bose Hubbard model using a mean field approximation (MFA) is studied. In the antiferromagnetic (AF) case, a smaller value of the staggered potential (SP) results in the charge and the spin density wave ordering along with the Mott insulator (MI) and the staggered superfluid (SSF) phases. While the competition between two types of the potential leads to the stabilization of the higher order MI and charge density wave (CDW) phases with increasing three‐body interaction strength. Further, the spin eigenvalue and nematic order parameters are calculated to scrutinize the spin singlet‐nematic formation in the MI and the CDW phases and spin population fractions to analyze the nature of the SSF phase. A signature of the spin density wave (SDW) pattern is also observed in the gapped phase lobes. In case of a purely three‐body interaction, the third and higher order insulating lobes become dominant with increasing staggered potential strength. Subsequently, all MFA phase diagrams are then nicely corroborated with the analytical results obtained using a perturbative expansion corresponding to the AF and ferromagnetic cases.
We study the effects of disorder on the spin dependent interaction term of a spinor Bose Hubbard model with a three body interaction potential. The signature of the Bose glass (BG) phase is observed by computing the fraction of the lattice sites having finite superfluid (SF) order parameter and non integer occupation densities. We obtain the phase diagram both for the antiferromagnetic (AF) and ferromagnetic (F) cases via a percolation analysis. In the AF case, the BG phase intervenes between the odd-even Mott insulating (MI) lobes (for example, the lobes corresponding to occupation densities, n=1 and (n=2) but not between the even-odd MI lobes. In the ferromagnetic case, the presence of the BG phase is observed between all the MI lobes irrespective of them being even or odd. The BG phase almost destroys the first MI lobe while the MI phase looks more stable than the SF phase both in the AF and F cases due to the presence of the three body interactions.
Abstract We study the effects of an attractive three-body interaction potential on a spin-1 ultracold Bose gas using the mean field approach (MFA). For an antiferromagnetic interaction, the third Mott insulator (MI) lobe is predominantly affected, where it completely engulfs the second and the fourth MI lobes at large values of interaction strength. However, no significant change is observed beyond the fourth MI lobe. The formation of the spin singlet (nematic) MI phase and the different order of phase transitions to the superfluid phase have been carefully scrutinized with the help of spin eigenvalues and the spin nematic order parameter. In the ferromagnetic case, the phase diagram shows similar features to that of a scalar Bose gas. We have compared our results on the MFA phase diagrams for both types of interaction potential via a perturbation expansion in both cases.
Abstract Cluster mean field theory for the two-dimensional spin-1 Bose–Hubbard model is applied to study superfluid (SF) to Mott insulator (MI) phase transitions and various magnetic phases that arise in the presence of spin-dependent anti-ferromagnetic and ferromagnetic interactions. This study clearly shows the nematic behavior of SF and odd-density MI phases, and a continuous phase transition between them for anti-ferromagnetic interaction. The even-density MI shows a nematic or singlet phase depending upon the strength of the interaction, and a continuous crossover between them. The SF to singlet MI transition is discontinuous. The dependence of cluster size on the critical on-site interaction ( U 0 C ) for SF to MI transitions is also studied. In the case of anti-ferromagnetic interaction, it is found that U 0 C for the SF to odd-density MI transition decreases with cluster size; however, no such changes are observed for the SF to singlet MI transition. In the case of ferromagnetic interactions, SF to MI transitions are continuous, and Mott lobes become enlarged with cluster size. Second order Rényi entanglement entropy (EE) is calculated in different phases. The results show that Rényi EE is large in the nematic MI phase.
We study the zero-temperature phase diagram of the disordered spin-111 Bose-Hubbard model in a two-dimensional square lattice. To this aim, we use a mean-field Gutzwiller ansatz and a probabilistic mean-field perturbation theory. The spin interaction induces two different regimes, corresponding to a ferromagnetic and antiferromagnetic order. In the ferromagnetic case, the introduction of disorder reproduces analogous features of the disordered scalar Bose-Hubbard model, consisting in the formation of a Bose glass phase between Mott insulator lobes. In the antiferromagnetic regime, the phase diagram differs more from the scalar case. Disorder in the chemical potential can lead to the disappearance of Mott insulator lobes with an odd-integer filling factor and, for sufficiently strong spin coupling, to Bose glass of singlets between even-filling Mott insulator lobes. Disorder in the spinor coupling parameter results in the appearance of a Bose glass phase only between the nnn and the n+1n+1n+1 lobes for nnn odd. Disorder in the scalar Hubbard interaction inhibits Mott insulator regions for occupation larger than a critical value.
Abstract We develop an inhomogeneous mean‐field theory for the extended Bose‐Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean‐field theory yields the phase diagram of the homogeneous extended Bose‐Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott‐insulator (MI), density‐wave (DW), and supersolid (SS) phases in the plane of the chemical potential µ and on‐site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest‐neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density‐wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold‐atom dipolar condensates in optical lattices in a confining potential.