We introduce three numerical methods for characterizing the topological phases of three-dimensional multiband Hubbard models based on twisted boundary conditions, Wilson loops, as well as the local topological marker. We focus on the half-filled, three-dimensional time-reversal-invariant Hofstadter model with finite spin-orbit coupling. Besides the weak and strong topological insulator phases we find a nodal line semimetal in the parameter regime between the two three-dimensional topological insulator phases. Using dynamical mean-field theory combined with the topological Hamiltonian approach we find stabilization of these three-dimensional topological states due to the Hubbard interaction. We study surface states which exhibit an asymmetry between left and right surface originating from the broken parity symmetry of the system. Our results set the stage for further research on inhomogeneous three-dimensional topological systems, proximity effects, topological Mott insulators, non-trivially linked nodal line semimetals and circuit-based quantum simulators.
We consider the three-body problem in a generic multiband lattice, and analyze the dispersion of the trimer states that are made of two spin-$\uparrow$ fermions and a spin-$\downarrow$ fermion due to an onsite attraction in between. Based on a variational approach, we first obtain the exact solution in the form of a set of coupled integral equations, and then reduce it to an eigenvalue problem. As an illustration we apply our theory to the sawtooth lattice, and numerically show that energetically-stable trimers are allowed in a two-band setting, which is in sharp contrast with the single-band …
We study the bound states of $N$ identical bosons that are described by a multiband Bose-Hubbard model with generic hoppings and an attractive onsite interaction. Using a variational approach, we first derive exact integral equations for the dimers, trimers, tetramers, and other multimers, and then apply them to a one-dimensional sawtooth model that features two bands. In particular we reveal the presence of not only the offsite dimer states which consist of two monomers on different sites even in the strong-coupling limit but also the offsite trimer states which consist of either a dimer on o…
We study phase diagrams of one-dimensional bosons with contact interactions in the presence of a lattice. We use the worm algorithm in continuous space and focus on the incommensurate superfluid Mott-insulator transition. Our results are compared to those from the one-band Bose-Hubbard model. When Wannier states are used to determine the Bose-Hubbard model parameters, the comparison unveils an apparent breakdown of the one-band description for strong interactions, even for the Mott-insulating state with an average of one particle per site ($n=1$) in deep lattices. We introduce an inverse confi…
We start with a variational approach and derive a set of coupled integral equations for the bound states of $N$ identical spin-$\uparrow$ fermions and a single spin-$\downarrow$ fermion in a generic multiband Hubbard Hamiltonian with an attractive onsite interaction. As an illustration we apply our integral equations to the one-dimensional sawtooth lattice up to $N \le 3$, i.e., to the $(3+1)$-body problem, and reveal not only the presence of tetramer states in this two-band model but also their quasi-flat dispersion when formed in a flat band. Furthermore, for $N = \{4, 5, \cdots, 10 \}$, our…
We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing only the chemical-potential disorder with the site-dependent hopping term. We compare the extension of the MI and the BG phase in both models using a combination of the local mean-field method and a Hartree-Fock-like procedure, as well as, the Gutzwiller-ansatz approach. We show analytical argument for the presence of triple points in the phase diagram of the m…
We study, using quantum Monte-Carlo simulations, the bosonic Kondo-Hubbard model in a two dimensional square lattice. We explore the phase diagram and analyse the mobility of particles and magnetic properties. At unit filling, the transition from a paramagnetic Mott insulator to a ferromagnetic superfluid appears continuous, contrary to what was predicted with mean field. For double occupation per site, both the Mott insulating and superfluid phases are ferromagnetic and the transition is still continuous. Multiband tight binding Hamiltonians can be realized in optical lattice experiments, whi…
We obtain a phase diagram of the spin imbalanced Hubbard model on the Lieb lattice, which is known to feature a flat band in its single-particle spectrum. Using the BCS mean-field theory for multiband systems, we find a variety of superfluid phases with imbalance. In particular, we find four different types FFLO phases, i.e. superfluid phases with periodic spatial modulation. They differ by the magnitude and direction of the centre-of-mass momentum of Cooper pairs. We also see a large region of stable Sarma phase, where the density imbalance is associated with zero Cooper pair momentum. In the…
We study the attractive Bose-Hubbard model with a tunable, on-site three-body constraint. It is shown that the critical behavior of the system undergoing a phase transition from pair-superfluid to superfluid at unit filling depends on the value of the three-body repulsion. In particular, we calculate critical exponents and the central charge governing the quantum phase transition.
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 th…
The experimental advances in cold atomic and molecular gases stimulate the investigation of lattice correlated systems beyond the conventional on-site Hubbard approximation, by possibly including multi-particle processes. We study fermionic extended Hubbard models in a one dimensional lattice with different types of particle couplings, including also three- and four-body interaction up to nearest neighboring sites. By using the Bosonization technique, we investigate the low-energy regime and determine the conditions for the appearance of ordered phases, for arbitrary particle filling. We find …
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 b…
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 antiferro…
We show that a two-atoms Bose-Hubbard model exhibits three different phases in the behavior of thermal entanglement in its parameter space. These phases are demonstrated to be traceable back to the existence of quantum phase transitions in the same system. Significant similarities between the behaviors of thermal entanglement and heat capacity in the parameter space are brought to light thus allowing to interpret the occurrence and the meaning of all these three phases.
A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity arrays is introduced, where the embedded two-level system in each cavity is replaced by a $Ξ$-type three-level system. We demonstrate that the resulting effective polariton-polariton interactions at each site are both two-body and three-body. By tuning the ratio of the two transition dipole matrix elements, we show that the strength and sign of the two-body interaction can be controlled whilst maintaining a three-body repulsion. We then proceed to demonstrate how different two-body and three-body interactions alter the me…
We analyze the energy spectrum of the three-site Bose-Hubbard model. It is shown that this spectrum is a mixture of the regular and irregular spectra associated with the regular and chaotic components of the classical Bose-Hubbard model. We find relative volumes of these components by using the pseudoclassical approach. Substituting these values in the Berry-Robnik distribution for the level spacing statistics we obtain good agreement with the numerical data.
An effective action for Bose-Hubbard model with two- and three-body on-site interaction in a square optical lattice is derived in the frame of a strong-coupling approach developed by Sengupta and Dupuis. From this effective action, superfluid-Mott insulator (MI) phase transition, excitation spectrum and momentum distribution for two phases are calculated by taking into account Gaussian fluctuation about the saddle-point approximation. In addition the effects of three-body interaction are also discussed.
The zero temperature properties of the generalized Bose-Hubbard model including three-body interactions are studied on a mean-field level. We obtain analytical results using the so-called perturbative mean-field method and more detailed numerical results using the Gutzwiller product state variational Ansatz. These two approaches yield equivalent results which compare well on a qualitative level with recent exact results obtained in the literature.
We apply the Bose-Hubbard Hamiltonian to a three-well system and show analytically that coherent transport via adiabatic passage (CTAP) of $N$ non-interacting particles across the chain is possible. We investigate the effect of detuning the middle well to recover CTAP when on-site interparticle interactions would otherwise disrupt the transport. The case of small interactions is restated using first-order perturbation theory to develop criteria for adibaticity that define the regime where CTAP is possible. Within this regime we investigate restricting the Hilbert space to the minimum necessary…
