Mott Insulator Lobes Research Articles

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

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.

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

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.

Anomalous pairing of bosons: Effect of multibody interactions in an optical lattice

An interesting first order type phase transition between Mott lobes has been reported in Phys. Rev. Lett. 109, 135302 (2012) for a two-dimensional Bose-Hubbard model in the presence of attractive three-body interaction. We re-visit the scenario in a system of ultracold bosons in a one-dimensional optical lattice using the density matrix renormalization group method and show that an unconventional pairing of particles occurs due to the competing two-body repulsive and three-body attractive interactions. This leads to a pair superfluid phase sandwiched between the Mott insulator lobes corresponding to densities $\rho=1$ and $\rho=3$ in the strongly interacting regime. We further extend our analysis to a two dimensional Bose-Hubbard model using the self consistent cluster-mean-field theory approach and confirm that the unconventional pair superfluid phase stabilizes in the region between the Mott lobes in contrast to the direct first order jump as predicted before. In the end we establish connection to the most general Bose-Hubbard model and analyse the fate of the pair superfluid phase in presence of an external trapping potential.

Spin-1 Bose–Hubbard model with two- and three-body interactions

We investigated the ground state of spin-1 bosons interacting under local two- and three-body interactions in one dimension by means of the density matrix renormalization group method. We found that the even–odd asymmetry will be obtained or not depending on the relative values of the two- and three-body interactions. The Mott insulator lobes are spin isotropic, the first showing a dimerized pattern and the second being composed of singlets. The three-body interactions disfavor a longitudinal polar superfluid and a quantum phase transition to a transverse polar superfluid occurs, which could be continuous or discontinuous.

Density-dependent hopping for ultracold atoms immersed in a Bose-Einstein-condensate vortex lattice

Both mixtures of atomic Bose-Einstein condensates and systems with atoms trapped in optical lattices have been intensely explored theoretically, mainly due to the exceptional developments on the experimental side. We investigate the properties of ultracold atomic impurities (bosons) immersed in a vortex lattice of a second Bose-condensed species. In contrast to the static optical-lattice configuration, the vortex lattice presents intrinsic dynamics given by its Tkachenko modes. These excitations induce additional correlations between the impurities, which consist in a long-range attractive potential and in a density-dependent hopping, described here in the framework of an extended Bose-Hubbard model. We compute the quantum phase diagram of the impurity species through a Gutzwiller ansatz and through the mean-field approach, and separately identify the effects of the two additional terms, i.e., the shift and the deformation of the Mott insulator lobes. The long-range attraction, in particular, induces the existence of a triple point in the phase diagram, in agreement with previous quantum Monte Carlo calculations [Chaviguri \emph{et al.}, Phys. Rev. A \textbf{95}, 053639 (2017)].

Quantum phases of a spin-1 ultracold Bose gas with three-body interactions

We study the effects of a three-body interaction potential on a spin-1 ultracold Bose gas using mean-field approach (MFA). For an antiferromagnetic (AF) interaction, we have found the existence of the odd-even asymmetry in the Mott insulating (MI) lobes in the presence of both the repulsive two- and three-body interactions. In case of a purely three-body repulsive interaction, the higher-order MI lobes stabilize against the superfluid phase. Also the spin nematic (singlet) formation occurs for all the odd (even) MI lobes for the former, while there is neither any asymmetry, nor spin nematic (singlet) formation being observed for the latter case. The results are confirmed after carefully scrutinizing the spin eigenvalue and spin nematic order parameter for both the cases. We have compared our MFA results with the analytic phase diagrams obtained using a perturbation mean-field (PMFA) expansion.

Spin‐1 Bose Hubbard Model with Nearest Neighbour Extended Interaction

AbstractA 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.

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

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.

Bose condensation in systems with p-particle tunneling and multi-body interactions

In this paper, we have studied a class of Hamiltonians that generalizes the Bose–Hubbard (BH) model of interacting bosons to include p-particle hopping as well as the multi-body interactions . While the case of two-body interaction and single-particle tunneling is well known, it is interesting to examine whether the resulting phase diagram for the general case has different features from that of the standard BH system. To this end we have applied a mean-field theory to locate critical lines, combined with the resolvent and Laplace transform method for the efficient calculation of the statistical sum for the quantum Hamiltonian. We have studied both ground state properties and temperature evolution of the phase diagram. Several new features, as an expansion of Mott insulator lobes for multi-body interaction and the emergence of a new insulating plateau for , have been demonstrated. These results may be of interest for experiments on cold atom systems in optical lattices.

Critical points of the Bose–Hubbard model with three-body local interaction

Abstract Using the density matrix renormalization group method, we study a one-dimensional system of bosons that interact with a local three-body term. We calculate the phase diagram for higher densities, where the Mott insulator lobes are surrounded by the superfluid phase. We also show that the Mott insulator lobes always grow as a function of the density. The critical points of the Kosterlitz–Thouless transitions were determined through the von Neumann block entropy, and its dependence on the density is given by a power law with a negative exponent.

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

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.

Reentrance and entanglement in the one-dimensional Bose-Hubbard model

Re-entrance is a novel feature where the phase boundaries of a system exhibit a succession of transitions between two phases A and B, like A-B-A-B, when just one parameter is varied monotonically. This type of re-entrance is displayed by the 1D Bose Hubbard model between its Mott insulator (MI) and superfluid phase as the hopping amplitude is increased from zero. Here we analyse this counter-intuitive phenomenon directly in the thermodynamic limit by utilizing the infinite time-evolving block decimation algorithm to variationally minimize an infinite matrix product state (MPS) parameterized by a matrix size chi. Exploiting the direct restriction on the half-chain entanglement imposed by fixing chi, we determined that re-entrance in the MI lobes only emerges in this approximate when chi >= 8. This entanglement threshold is found to be coincident with the ability an infinite MPS to be simultaneously particle-number symmetric and capture the kinetic energy carried by particle-hole excitations above the MI. Focussing on the tip of the MI lobe we then applied, for the first time, a general finite-entanglement scaling analysis of the infinite order Kosterlitz-Thouless critical point located there. By analysing chi's up to a very moderate chi = 70 we obtained an estimate of the KT transition as t_KT = 0.30 +/- 0.01, demonstrating the how a finite-entanglement approach can provide not only qualitative insight but also quantitatively accurate predictions.

Ground-state phase diagram of spin-12bosons in a two-dimensional optical lattice

We study a two-species bosonic Hubbard model on a two-dimensional square lattice by means of quantum Monte Carlo simulations. In addition to the usual contact repulsive interactions between the particles, the Hamiltonian has an interconversion term which allows the transformation of two particles from one species to the other. The phases are characterized by their solid or superfluid properties and by their polarization, i.e., the difference in the populations. When interspecies interactions are smaller than the intraspecies ones, the system is unpolarized, whereas in the opposite case the system is unpolarized in even Mott insulator lobes and polarized in odd Mott lobes and also in the superfluid phase. We show that in the latter case the transition between the Mott insulator of total density 2 and the superfluid can be of either second or first order depending on the relative values of the interactions, whereas the transitions are continuous in all other cases.

Disordered spinor Bose-Hubbard model

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.

Phase diagrams of the Bose-Fermi-Hubbard model: Hubbard operator approach

The phase transitions in the Bose-Fermi-Hubbard model are investigated. The boson Green's function is cal- culated in the random phase approximation (RPA) and the formalism of the Hubbard operators is used. The regions of existence of the superuid and Mott insulator phases are established and the (; t) (the boson chemical potential vs. hopping parameter) phase diagrams are built at different values of boson-fermion in- teraction constant (in the regimes of x ed chemical potential or x ed concentration of fermions). The effect of temperature change on this transition is analyzed and the phase diagrams in the (T; ) plane are constructed. The role of thermal activation of the ion hopping is investigated by taking into account the temperature depen- dence of the transfer parameter. The reconstruction of the Mott-insulator lobes due to this effect is analyzed. parameters of the BFHM which describes these objects can be tuned in experiments and results of theoretical calculations can be tested in practice. Dieren t theoretical approaches were used to investigate the BFHM: mean eld theory (2), strong coupling approach (3), density matrix renormalization group (4), quantum Monte Carlo (5) and others. Another example of systems which can be described by the Bose-Fermi-Hubbard-type Hamil- tonian are intercalated crystals (for example, TiO2 intercalated by Li ions). In such systems the impurity ions and electrons play the role of the bosons and fermions, respectively. A lattice gas type models are also used for the description of ionic conductors (7{9). In (10) the pseudospin-electron model of intercalation was formulated and thermodynamics of the model was investigated in the mean eld approximation. It was shown that due to the presence of electrons the eectiv e inter- action between ions is generated and the character of this interaction depends on the lling of the electron band (when the chemical potential of the electrons is near the band edges, the rst order phase transition between uniform phases or phase separation in the regime of the xed electron concentration takes place; such an eect is important when constructing batteries (11)). In this work we consider the BFHM and propose a method for calculation of correlation func- tions and average values of boson and fermion concentrations. The method is based on the intro- duction of Hubbard operators acting in the on-site basis of states and is similar to the composite fermion approach used in (2) (the composite fermions are formed by a fermion and bosons or bosonic holes) but is more general and universal. Introducing the on-site Hubbard operators we can employ a known technique developed for the calculation of a correlation (Green's) function built on these operators, for example, equation of motion method (12) or diagrammatic approach based on the corresponding Wick's theorem (13). In this paper we use the rst of them. As a rst

Effects of fermions on the superfluid-insulator phase diagram of the Bose-Hubbard model

Building on the work of Fisher et al. [Phys. Rev. B 40, 546 (1989)], we develop the perturbation theory for the Bose-Hubbard model and apply it to calculate the effects of a degenerate gas of spin-polarized fermions interacting by contact interactions with the constituent bosons. For the single-band Bose-Hubbard model, we find that the net effect of the screening of the boson on-site interaction by the fermions is to suppress the Mott-insulating lobes in the Bose-Hubbard phase diagram. For the more general multiband model, we find that, in addition to the fermion screening effects, the virtual excitations of the bosons to the higher Bloch bands, coupled with the contact interactions with the fermions, result in an effective increase (decrease) of the boson on-site repulsion (hopping parameter). If the higher-band renormalization of the boson parameters is dominant over the fermion screening of the interaction, the Mott-insulating lobes in the Bose-Hubbard phase diagram are enhanced for either sign of the Bose-Fermi interactions, consistent with the recent experiments.

Phase diagrams of the Bose-Hubbard model at finite temperature

The phase transitions in the Bose-Hubbard model are investigated. A single-particle Green’s function is calculated in the random phase approximation and the formalism of the Hubbard operators is used. The regions of existence of the superuid and Mott insulator phases are established and the (; t) (the chemical potential n transfer parameter) phase diagrams are built. The effect of temperature change on this transition is analyzed and the phase diagram in the (T; ) plane is constructed. The role of thermal activation of the ion hopping is investigated by taking into account the temperature dependence of the transfer parameter. The reconstruction of the Mott-insulator lobes due to this effect is analyzed.

Superfluid to Mott-insulator transition in an anisotropic two-dimensional optical lattice

We study the superfluid to Mott-insulator transition of bosons in an optical anisotropic lattice by employing the Bose-Hubbard model living on a two-dimensional lattice with anisotropy parameter κ. The compressible superfluid state and incompressible Mott-insulator (MI) lobes are efficiently described analytically, using the quantum U(1) rotor approach. The ground state phase diagram showing the evolution of the MI lobes is quantified for arbitrary values of κ, corresponding to various kind of lattices: from square, through rectangular to almost one-dimensional.

Superfluid to Mott‐insulator transition in an anisotropic two‐dimensional optical lattice

AbstractWe study the superfluid to Mott‐insulator transition of bosons in an optical anisotropic lattice by employing the Bose‐Hubbard model living on a two‐dimensional lattice with anisotropy parameter κ. The compressible superfluid state and incompressible Mott‐insulator (MI) lobes are efficiently described analytically, using the quantum U(1) rotor approach. The ground state phase diagram showing the evolution of the MI lobes is quantified for arbitrary values of κ, corresponding to various kind of lattices: from square, through rectangular to almost one‐dimensional.

Canonical trajectories and critical coupling of the Bose-Hubbard Hamiltonian in a harmonic trap

Quantum Monte Carlo (QMC) simulations and the local density approximation (LDA) are used to map the constant particle number (canonical) trajectories of the Bose-Hubbard Hamiltonian confined in a harmonic trap onto the $(\ensuremath{\mu}∕U,t∕U)$ phase diagram of the uniform system. Generically, these curves do not intercept the tips of the Mott insulator lobes of the uniform system. This observation necessitates a clarification of the appropriate comparison between critical couplings obtained in experiments on trapped systems with those obtained in QMC simulations. The density profiles and visibility are also obtained along these trajectories. Density profiles from QMC in the confined case are compared with LDA results.