Mott Lobes Research Articles

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.

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

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 (U0C) for SF to MI transitions is also studied. In the case of anti-ferromagnetic interaction, it is found that U0C 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.

Phase transitions and spin excitations of spin-1 bosons in optical lattice

We investigate ground state properties of spin-1 bosonic system trapped in optical lattice with extended standard basis operator (SBO) method. For both ferromagnetic ($U_2<0$) and antiferromagnetic ($U_2>0$) systems, we analytically figure out the symmetry properties in Mott-insulator and superfluid phases, which would provide a deeper insight into the MI-SF phase transition process. Then by applying self-consistent approach to the method, we include the effect of quantum and thermal fluctuations and derive the MI-SF transition phase diagram, which is in quantitative agreement with recent Monte-Carlo simulation at zero temperature, and at finite temperature, we find the underestimation of finite-temperature-effect in the mean-field approximation method. If we further consider the spin excitations in the insulating states of spin-1 system in external field, distinct spin phases are expected. Therefore, in the Mott lobes with $n=1$ and $n=2$ atoms per site, we give analytical and numerical boundaries of the singlet, nematic, partially magnetic and ferromagnetic phases in the magnetic phase diagrams.

Phase diagrams of antiferromagnetic spin-1 bosons on a square optical lattice with the quadratic Zeeman effect

We study the quadratic Zeeman effect (QZE) in a system of antiferromagnetic spin-1 bosons on a square lattice and derive the ground-state phase diagrams by means of quantum Monte Carlo simulations and mean field treatment. The QZE imbalances the populations of the magnetic sublevels $\sigma=\pm1$ and $\sigma=0$, and therefore affects the magnetic and mobility properties of the phases. Both methods show that the tip of the even Mott lobes, stabilized by singlet state, is destroyed when turning on the QZE, thus leaving the space to the superfluid phase. Contrariwise, the tips of odd Mott lobes remain unaffected. Therefore, the Mott-superfluid transition with even filling strongly depends on the strength of the QZE, and we show that the QZE can act as a control parameter for this transition at fixed hopping. Using quantum Monte Carlo simulations, we elucidate the nature of the phase transitions and examine in detail the nematic order: the first-order Mott-superfluid transition with even filling observed in the absence of QZE becomes second order for weak QZE, in contradistinction to our mean-field results which predict a first-order transition in a larger range of QZE. Furthermore, a spin nematic order with director along the $z$ axis is found in the odd Mott lobes and in the superfluid phase for energetically favored $\sigma=\pm1$ states. In the superfluid phase with even filling, the $xy$ components of the nematic director remain finite only for moderate QZE.

Phase transitions of the coherently coupled two-component Bose gas in a square optical lattice

We investigate properties of an ultracold, two-component bosonic gas in a square optical lattice at unit filling. In addition to density-density interactions, the atoms are subject to coherent light-matter interactions that couple different internal states. We examine the influence of this coherent coupling on the system and its quantum phases by using Gutzwiller mean field theory as well as bosonic dynamical mean field theory. We find that the interplay of strong inter-species repulsion and coherent coupling affects the Mott insulator to superfluid transition and shifts the tip of the Mott lobe toward higher values of the tunneling amplitude. In the strongly interacting Mott regime, the resulting Bose-Hubbard model can be mapped onto an effective spin Hamiltonian that offers additional insights into the observed phenomena.

Superfluid–Mott-insulator transition in superconducting circuits with weak anharmonicity

We investigate theoretically the ground-state property of a two-dimensional array of superconducting circuits including the on-site superconducting qubits (SQs) with weak anharmonicity. In particular, we analyse the influence of this anharmonicity on the Mott insulator to superfluid quantum phase transition. The complete ground-state phase diagrams are presented under the mean field approximation. Interestingly, the anharmonicity of SQs affects the Mott lobes enormously, and the single excitation Mott lobe disappears when the anharmonicity become zero. Our results can be used to guide the implementations of quantum simulations using the superconducting circuits, which have nice integrating and flexibility.

Quantum phase transitions of light in a dissipative Dicke-Bose-Hubbard model

The impact that the environment has on the quantum phase transition of light in the Dicke-Bose-Hubbard model is investigated. Based on the quasibosonic approach, mean-field theory, and perturbation theory, the formulation of the Hamiltonian, the eigenenergies, and the superfluid order parameter are obtained analytically. Compared with the ideal cases, the order parameter of the system evolves with time as the photons naturally decay in their environment. When the system starts with the superfluid state, the dissipation makes the photons more likely to localize, and a greater hopping energy of photons is required to restore the long-range phase coherence of the localized state of the system. Furthermore, the Mott lobes depend crucially on the numbers of atoms and photons (which disappear) of each site, and the system tends to be classical with the number of atoms increasing; however, the atomic number is far lower than that expected under ideal circumstances. As there is an inevitable interaction between the coupled-cavity array and its surrounding environment in the actual experiments, the system is intrinsically dissipative. The results obtained here provide a more realistic image for characterizing the dissipative nature of quantum phase transitions in lossy platforms, which will offer valuable insight into quantum simulation of a dissipative system and which are helpful in guiding experimentalists in open quantum systems.

Quantum phase diagrams of the Jaynes–Cummings Hubbard models in non-rectangular lattices

In this paper, we investigate systematically the quantum phase transition between the Mott-insulator and superfluid states of the Jaynes–Cummings Hubbard model in triangular, square, honeycomb and kagomé lattices. With the help of Green’s function method, by treating the hopping term in the Jaynes–Cummings Hubbard model as perturbation, we calculate the phase boundaries of Jaynes–Cummings Hubbard models on different geometrical lattices analytically up to second order for both detuning and . It is shown that the Mott phase becomes more unstable when increasing the polariton number n. Meanwhile, the Mott lobe of n = 0 is enlarged while other Mott lobes shrink as the detuning parameter increases.

Effects of higher-order energy bands and temperature on the bosonic Mott insulator in a periodically modulated lattice

We show that a certain class of higher-order excitations in ultracold atoms experiments can be described by straightforward extension of the standard strong coupling approach in the coherent state path integral formalism. It is achieved by theoretical analysis of energy absorption spectroscopy in the three-dimensional system of strongly correlated bosons described by the Bose-Hubbard model. In particular, for unit filling, an explicit form of the single-particle Mott insulator Green function at finite temperatures is derived which goes beyond the standard Hubbard bands description. Moreover, for relevant densities, we calculated the energy absorption rate and performed thermometry on rubidium atomic cloud gas by using previously obtained experimental data. Within the local density approximation, we explain that in such systems the nature of absorption spectrum depends significantly on local chemical potential: (a) the crossover region between lobes is characterized by different types of particle-hole excitations from neighboring Mott lobes and (b) origin of higher-order energy excitations changes from hole type to particle type for higher bosonic densities.

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

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.

Critical points of the anyon-Hubbard model

Anyons are particles with fractional statistics that exhibit a nontrivial change in the wavefunction under an exchange of particles. Anyons can be considered to be a general category of particles that interpolate between fermions and bosons. We determined the position of the critical points of the one-dimensional anyon-Hubbard model, which was mapped to a modified Bose-Hubbard model where the tunneling depends on the local density and the interchange angle. We studied the latter model by using the density matrix renormalization group method and observed that gapped (Mott insulator) and gapless (superfluid) phases characterized the phase diagram, regardless of the value of the statistical angle. The phase diagram for higher densities was calculated and showed that the Mott lobes increase (decrease) as a function of the statistical angle (global density). The position of the critical point separating the gapped and gapless phases was found using quantum information tools, namely the block von Neumann entropy. We also studied the evolution of the critical point with the global density and the statistical angle and showed that the anyon-Hubbard model with a statistical angle $\theta =\pi/4$ is in the same universality class as the Bose-Hubbard model with two body interactions.

Influence of counter-rotating interaction on quantum phase transition in Dicke-Hubbard lattice: an extended coherent-state approach

We investigate the ground state behavior of the Dicke-Hubbard model including counter-rotating-terms. By generalizing an extended coherent state approach within mean-field theory, we self-consistently obtain the ground state energy and delocalized order parameter. Localization-delocalization quantum phase transition of photons is clearly observed by breaking the parity symmetry. Particularly, Mott lobes are fully suppressed, and the delocalized order parameter shows monotonic enhancement by increasing qubit-cavity coupling strength, in sharp contrast to the Dicke-Hubbard model under rotating-wave approximation. Moreover, the corresponding phase boundaries are stabilized by decreasing photon hopping strength, compared to the Rabi-Hubbard model.

Hubbard Model for Atomic Impurities Bound by the Vortex Lattice of a Rotating Bose-Einstein Condensate.

We investigate cold bosonic impurity atoms trapped in a vortex lattice formed by condensed bosons of another species. We describe the dynamics of the impurities by a bosonic Hubbard model containing occupation-dependent parameters to capture the effects of strong impurity-impurity interactions. These include both a repulsive direct interaction and an attractive effective interaction mediated by the Bose-Einstein condensate. The occupation dependence of these two competing interactions drastically affects the Hubbard model phase diagram, including causing the disappearance of some Mott lobes.

Competing ground states of strongly correlated bosons in the Harper-Hofstadter-Mott model

Using an efficient cluster approach, we study the physics of two-dimensional lattice bosons in a strong magnetic field in the regime where the tunneling is much weaker than the on-site interaction strength. We study both dilute, hard core bosons at filling factors much smaller than unity occupation per site, and the physics in the vicinity of the superfluid-Mott lobes as the density is tuned away from unity. For hardcore bosons, we carry out extensive numerics for a fixed flux per plaquette $\phi=1/5$ and $\phi = 1/3$. At large flux, the lowest energy state is a strongly correlated superfluid, analogous to He-$4$, in which the order parameter is dramatically suppressed, but non-zero. At filling factors $\nu=1/2,1$, we find competing incompressible states which are metastable. These appear to be commensurate density wave states. For small flux, the situation is reversed, and the ground state at $\nu = 1/2$ is an incompressible density-wave solid. Here, we find a metastable lattice supersolid phase, where superfluidity and density-wave order coexist. We then perform careful numerical studies of the physics near the vicinity of the Mott lobes for $\phi = 1/2$ and $\phi = 1/4$. At $\phi = 1/2$, the superfluid ground state has commensurate density-wave order. At $\phi = 1/4$, incompressible phases appear outside the Mott lobes at densities $n = 1.125$ and $n = 1.25$, corresponding to filling fractions $\nu = 1/2$ and $1$ respectively. These phases, which are absent in single-site mean-field theory are metastable, and have slightly higher energy than the superfluid, but the energy difference between them shrinks rapidly with increasing cluster size, suggestive of an incompressible ground state. We thus explore the interplay between Mott physics, magnetic Landau levels, and superfluidity, finding a rich phase diagram of competing compressible and incompressible states.

Inter-species entanglement of Bose–Bose mixtures trapped in optical lattices

In the present work we discuss inter-species entanglement in Bose–Bose mixtures trapped in optical lattices. This work is motivated by the observation that, in the presence of a second component, the MI lobe shifts differently on the hole- and particle-side with respect to the Mott lobe of the single species system (Guglielmino et al 2010 Phys. Rev. A 82 021601; Capogrosso-Sansone et al 2011 Laser Phys. 21 1443). We use perturbation theory, formulated in a Hilbert space decomposed by means of lattice symmetries, in order to show that the nonuniform shift of the Mott lobe is a manifestation of inter-species entanglement which differs in the lowest excited states to remove and add a particle. Our results indicate that inter-species entanglement in mixtures can provide a new perspective in understanding quantum phase transitions. To validate our approach, we compare our results from perturbation theory with quantum Monte Carlo simulations.

Magnetic phase transition in coherently coupled Bose gases in optical lattices

We describe the ground state of a gas of bosonic atoms with two coherently coupled internal levels in a deep optical lattice in a one dimensional geometry. In the single-band approximation this system is described by a Bose-Hubbard Hamiltonian. The system has a superfluid and a Mott insulating phase which can be either paramagnetic or ferromagnetic. We characterize the quantum phase transitions at unit filling by means of a density matrix renormalization group technique and compare it with a mean-field approach. The presence of the ferromagnetic Ising-like transition modifies the Mott lobes. In the Mott insulating region the system maps to the ferromagnetic spin-1/2 XXZ model in a transverse field and the numerical results compare very well with the analytical results obtained from the spin model. In the superfluid regime quantum fluctuations strongly modify the phase transition with respect to the well established mean-field three dimensional classical bifurcation.

Mott lobes evolution of the spin-1 Bose-Hubbard model

We study spin-1 bosons confined in a one-dimensional optical lattice, taking into consideration both ferromagnetic and antiferromagnetic interaction. Using the density matrix renormalization group, we determine the phase diagram for the two firsts lobes and report the evolution of the first and second Mott lobes with respect to the spin-exchange interaction parameter (U2). We determine that for the antiferromagnetic case, the first lobe is suppressed while the second grows as |U2| increases. For the ferromagnetic case, the first and second Mott lobes are suppressed by the spin-exchange interaction parameter. We propose an expresion to describe the evolution of the critical point with the increase in |U2| for both cases.

Density matrix renormalization group study of the Anyon-Hubbard model

Recently optical lattices allow us to observe phase transition without the uncertainty posed by complex materials, and the simulations of these systems are an excellent bridge between materials-based condensed matter physics and cold atoms. In this way, the computational physics related to many-body problems have increased in importance. Using the density matrix renormalization group method, we studied a Hubbard model for anyons, which is an equivalent to a variant of the Bose-Hubbard model in which the bosonic hopping depends on the local density. This is an exact mapping between anyons and bosons in one dimension. The anyons interlope between bosons and fermions. For two anyons under particle exchange, the wave function acquires a fractional phase eiθ. We conclude that this system exhibits two phases: Mott-insulator and superfluid. We present the phase diagram for some angles. The Mott lobe increases with an increase of the statistical. We observed a reentrance phase transition for all lobes. We showed that the model studied is in the same universality class as the Bose-Hubbard model with two-body interactions.

Bose and Mott glass phases in dimerized quantum antiferromagnets

We examine the effects of disorder on dimerized quantum antiferromagnets in a magnetic field, using the mapping to a lattice gas of hard-core bosons with finite-range interactions. Combining a strong-coupling expansion, the replica method, and a one-loop renormalization group analysis, we investigate the nature of the glass phases formed. We find that away from the tips of the Mott lobes, the transition is from a Mott insulator to a compressible Bose glass, however the compressibility at the tips is strongly suppressed. We identify this finding with the presence of a rare Mott glass phase not previously described by any analytic theory for this model and demonstrate that the inclusion of replica symmetry breaking is vital to correctly describe the glassy phases. This result suggests that the formation of Bose and Mott glass phases is not simply a weak localization phenomenon but is indicative of much richer physics. We discuss our results in the context of both ultracold atomic gases and spin-dimer materials.

Extended Bose-Hubbard model in a shaken optical lattice

We study an extended Bose-Hubbard model with next-nearest-neighbor (NNN) hopping in a shaken optical lattice. We show how mean-field phase diagram evolves with the change of NNN hopping amplitude $t_{2}$, which can be easily tuned via shaking amplitude. As $t_{2}$ increases, a $Z_{2}$-symmetry-breaking superfluid ($Z_{2}$SF) phase emerges at the bottom of the Mott lobs. The tricritical points between normal superfluid, $Z_{2}$SF, and Mott insulator (MI) phases are identified. We further demonstrate the tricritical point can be tuned to the tip of the Mott lobe, in which case a new critical behavior has been predicted. Within random-phase approximation, excitation spectra in the three phases are obtained, which indicate how the phase transitions occur.