In quantum many-body system, dimensionality plays a critical role on type of the quantum phase transition. In order to study the quantum system during dimensional crossover, we studied the Bose-Hubbard model on cubic lattice with anisotropic hopping by using the high order symbolic strong coupling expansion method. The analytic series expanded boundaries between the Mott-insulator and superfluid phase up to eighth order are calculated. The critical exponents are extracted by Padé re-summation method, which clearly shows the dimensional crossover behavior. Meanwhile, the critical points at commensurate filling can also be obtained, and they match well with the prediction of renormalization group theory. The scaling of the gap energy and whole phase diagram are given at last, and they can be taken as the benchmark for experiment and numerical simulations in the future study.
Bosonic lattice systems with non-trivial interactions represent an intriguing platform to study exotic phases of matter. Here, we study the effects of extended correlated hopping processes in a system of bosons trapped in a lattice geometry. The interplay between single particle tunneling terms, correlated hopping processes and on-site repulsion is studied by means of a combination of exact diagonalization, strong coupling expansion and cluster mean field theory. We identify a rich ground state phase diagram where, apart the usual Mott and superfluid states, superfluid phases with interesting …
We study systematically an extended Bose-Hubbard model on the triangular lattice by means of a meanfield method based on the Gutzwiller ansatz. Pair hopping terms are explicitly included and a three-body constraint is applied. The ground-state phase diagram and a variety of quantum phase transitions are investigated in great detail. In particular, we show the existence and stability of the pair supersolid phase.
We study a two-leg fermionic Hubbard ladder model with a state-dependent hopping. We find that, contrary to the case without a state-dependent hopping, for which the system has a superfluid nature regardless of the sign of the interaction at incommensurate filling, in the presence of such a hopping a spin-triplet superfluid, spin- density wave and charge-density wave phases emerge. We examine our results in the light of recent experiments on periodically-driven optical lattices in cold atoms. We give protocols allowing us to realize the spin-triplet superfluid elusive in the cold atoms.
We investigate the effects of an extended Bose-Hubbard model with a long range hopping term on the Mott insulator-superfluid quantum phase transition. We consider the effects of a power law decaying hopping term and show that the Mott phase is shrinked in the parameters' space. We provide an exact solution for one dimensional lattices and then two approximations for higher dimensions, each one valid in a specific range of the power law exponent: a continuum approximation and a discrete one. Finally, we extend these results to a more realistic situation, where the long range hopping term is mad…
In this paper, we study Bose-Hubbard models on the square and honeycomb lattices with complex hopping amplitudes, which are feasible by recent experiments of cold atomic gases in optical lattices. To clarify phase diagrams, we use an extended quantum Monte-Carlo simulations (eQMC). For the system on the square lattice, the complex hopping is realized by an artificial magnetic field. We found that vortex-solid states form for certain set of magnetic field, i.e., the magnetic field with the flux quanta per plaquette $f=p/q$, where $p$ and $q$ are co-prime natural numbers. For the system on the h…
We consider a strongly repulsive two-component Fermi gas in a one-dimensional (1D) optical lattice described in terms of a Hubbard Hamiltonian. We analyze the response of the system to a periodic modulation of the hopping amplitude in presence of large two body interaction. By (essentially) exact simulations of the time evolution, we find a non-trivial double occupancy frequency dependence. We show how the dependence relates to the spectral features of the system given by the Bethe ansatz. The discrete nature of the spectrum is clearly reflected in the double occupancy after long enough modula…
We compute the ground state phase diagram of the 2d Bose-Hubbard model with anisotropic hopping using quantum Monte Carlo simulations, connecting the 1d to the 2d system. We find that the tip of the lobe lies on a curve controlled by the 1d limit over the full anisotropy range while the universality class is always the same as in the isotropic 2d system. This behavior can be derived analytically from the lowest RG equations and has a form typical for the underlying Kosterlitz-Thouless transition in 1d. We also compute the phase boundary of the Mott lobe for strong anisotropy and compare it to …
Recently precise results for the boundary between the Mott insulator phase and the superfluid phase of the homogeneous Bose-Hubbard model have become available for arbitrary integer filling factor g and any lattice dimension d > 1. We use these data for demonstrating that the critical hopping parameters obey a scaling relationship which allows one to map results for different g onto each other. Unexpectedly, the mean-field result captures the dependence of the exact critical parameters on the filling factor almost fully. We also present an approximation formula which describes the critical par…
We study the real time dynamics of the Bose Hubbard model in the presence of time-dependent hopping allowing for a finite temperature initial state. We use the Schwinger-Keldysh technique to find the real-time strong coupling action for the problem at both zero and finite temperature. This action allows for the description of both the superfluid and Mott insulating phases. We use this action to obtain dynamical equations for the superfluid order parameter as hopping is tuned in real time so that the system crosses the superfluid phase boundary. We find that under a quench in the hopping, the s…
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…
Frustration and quantum entanglement are two exotic quantum properties in quantum many-body systems. However, despite several efforts, an exact relation between them remains elusive. In this work, we explore the relationship between frustration and quantum entanglement in a physical model describing strongly correlated ultracold bosonic atoms in optical lattices. In particular, we consider the one-dimensional Bose-Hubbard model comprising both nearest-neighbor ($t_{1}$) and frustrated next-nearest neighbor ($t_{2}$) hoppings and examine how the interplay of onsite interaction ($U$) and hopping…
We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of large-scale Quantum Monte Carlo simulations, the ground-state phase diagram are studied. We find a continuous transition between the atomic superfluid phase and the pair superfluid when the ratio of the atomic hopping and the atom-pair hopping is adapted. We then focus on the interplay among the atom-pair hopping, the on-site repulsion and the nearest-neighbor repulsion. With on-site repulsion present, we observe first …
The high-barrier quantum tunneling regime of a Bose-Einstein condensate confined in a ring-shaped optical lattice is investigated. By means of a change of basis transformation, connecting the set of `vortex' Bloch states and a Wannier-like set of localized wave functions, we derive a generalized Bose-Hubbard Hamiltonian. In addition to the usual hopping rate terms, such a Hamiltonian takes into account interaction-driven tunneling processes, which are shown to play a principal role at high filling factors, when the standard hopping rate parameter turns out to be negative. By calculating the en…
Recent experiments show that periodic modulations of cold atoms in optical lattices may be used to engineer and explore interesting models. We show that double modulation, combining lattice shaking and modulated interactions allows for the engineering of a much broader class of lattice models with correlated hopping, which we study for the particular case of one-dimensional systems. We show, in particular, that by using this double modulation it is possible to study Hubbard models with asymmetric hopping, which, contrary to the standard Hubbard model, present insulating phases with both parity…
We investigate formation and condensation of fermion pairs in cold-atom quantum simulators for extended Hubbard models ($UV$ models) with body-centered-cubic (BCC) optical lattices in the dilute limit, predicting small and light pairs. Pair mass, radius, and binding conditions are calculated, and used to compute transition temperatures. We predict that: (a) local pairs form in BCC optical lattices and binding energies can be large; (b) for particular cases where onsite $U$ and intersite $V$ are attractive with similar size, pairs are both small and light; and (c) pairs of $^6$Li atoms Bose--Ei…
Recent experiments revealed the importance of higher-band effects for the Mott insulator (MI) -- superfluid transition (SF) of ultracold bosonic atoms or mixtures of bosons and fermions in deep optical lattices [Best \emph{et al.}, PRL \textbf{102}, 030408 (2009); Will \emph{et al.}, Nature \textbf{465}, 197 (2010)]. In the present work, we derive an effective lowest-band Hamiltonian in 3D that generalizes the standard Bose-Fermi Hubbard model taking these effects as well as nonlinear corrections of the tunneling amplitudes mediated by interspecies interactions into account. It is shown that a…
In this paper we study the relation between long cycles and Bose-Einstein condensation in the Infinite-Range Bose-Hubbard Model. We obtain an expression for the cycle density involving the partition function for a Bose-Hubbard Hamiltonian with a single-site correction. Inspired by the Approximating Hamiltonian method we conjecture a simplified expression for the short cycle density as a ratio of single-site partition functions. In the absence of condensation we prove that this simplification is exact and use it to show that in this case the long-cycle density vanishes. In the presence of conde…
The Properties of the Mott insulator to superfluid phase transition are obtained through the fermionic approximation in the Jaynes-Cummings-Hubbard model on linear, square, SC, FCC, and BCC Bravais lattices. For varying excitation number and atom-cavity frequency detuning. We find that the Mott lobes and the critical hopping are not scalable only for the FCC lattice. At the large excitation number regime, the critical hopping is scalable for all the lattices and it does not depend on the detuning.
We apply the bosonization technique to derive the phase diagram of a balanced unit density two-component dipolar Fermi gas in a one dimensional lattice geometry. The considered interaction processes are of the usual contact and dipolar long-range density-density type together with peculiar correlated hopping terms which can be generated dynamically. Rigorous bounds for the transition lines are obtained in the weak coupling regime. In addition to the standard bosonization description, we derive the low energy phase diagram taking place when part of the interaction is embodied non-perturbatively…
Experimental realizations of disorder in optical lattices generate a distribution of the Bose-Hubbard (BH) parameters, like on-site potentials, hopping strengths, and interaction energies. We analyze this distribution for bosons in a bichromatic quasi-periodic potential by determining the generalized Wannier functions and calculating the corresponding BH parameters. Using a local mean-field cluster analysis, we study the effect of the corresponding disorder on the phase diagrams. We find a substantial amount of disorder in the hopping strengths, which produces strong deviations from the phase …
In this letter we consider quantum phases and the phase diagram of a Fermi Hubbard model under periodic driving that has been realized in recent cold atom experiments, in particular, when the driving frequency is resonant with the interaction energy. Due to the resonant driving, the effective Hamiltonian contains a correlated hopping term where the density occupation strongly modifies the hopping strength. Focusing on half filling, in addition to the charge and spin density wave phases, large regions of ferromagnetic phase and phase separation are discovered in the weakly interacting regime. T…
We study a simple model of interacting bosons on a d-dimensional cubic lattice whose dynamics conserves both total boson number and total boson dipole moment. This model provides a simple framework in which several remarkable consequences of dipole conservation can be explored. As a function of chemical potential and hopping strength, the model can be tuned between gapped Mott insulating phases and various types of gapless condensates. The condensed phase realized at large hopping strengths, which we dub a Bose-Einstein insulator, is particularly interesting: despite having a Bose condensate, …
We study the Hubbard model with non-Hermitian asymmetric hopping terms. The conjugate hopping terms are introduced for two spin components so that the negative sign is canceled out. This ensures that the quantum Monte Carlo simulation is free from the negative sign problem. We analyze the antiferromagnetic order and its suppression by the non-Hermiticity.
Phase transitions in systems described by Bose-Fermi-Hubbard model on a lattice with two nonequivalent sublattices are investigated in this work. The case of hard-core bosons is considered and pseudospin formalism is used. Phase diagrams are built in the plain of chemical potential of the bosons-bosonic hopping parameter. It is shown that in the case of anisotropic hopping, the region of the supersolid phase existence is possible for a smaller parameter space.
We investigate exotic supersolid phases in the extended Bose-Hubbard model with infinite projected entangled-pair state, numerical exact diagonalization, and mean-field theory. We demonstrate that many different supersolid phases can be generated by changing signs of hopping terms, and the interactions along with the frustration of hopping terms are important to stabilize those supersolid states. We argue the effect of frustration introduced by the competition of hopping terms in the supersolid phases from the mean-field point of view. This helps to give a clearer picture of the background mec…
We discuss analytic approximations to the ground state phase diagram of the homogeneous Jaynes-Cummings-Hubbard (JCH) Hamiltonian with general short-range hopping. The JCH model describes e.g. radial phonon excitations of a linear chain of ions coupled to an external laser field tuned to the red motional sideband with Coulomb mediated hopping or an array of high-$Q$ coupled cavities containing a two-level atom and photons. Specifically we consider the cases of a linear array of coupled cavities and a linear ion chain. We derive approximate analytic expressions for the boundaries between Mott-i…
Superconductivity in the repulsive Hubbard model on different geometries induced by density-assisted hopping
University of Bonn（波恩大学）；ENSL, CNRS, Laboratoire de Physique（里昂高等师范学院，法国国家科学研究中心，物理实验室）；Physics Department “E. R. Caianiello” and CNR-SPIN, Universitá degli Studi di Salerno, INFN, Gruppo Collegato di Salerno（萨莱诺大学“E.R.卡亚涅洛”物理系及CNR-SPIN，意大利国家核物理研究所萨莱诺联合小组）；Universitá degli Studi di Salerno（萨莱诺大学）
We study the phase diagram of the asymmetric Hubbard model (AHM), which is characterized by different values of the hopping for the two spin projections of a fermion or equivalently, two different orbitals. This model is expected to provide a good description of a mass-imbalanced cold fermionic mixture in a 3D optical lattice. We use the dynamical mean field theory to study various physical properties of this system. In particular, we show how orbital-selective physics, observed in multi-orbital strongly correlated electron systems, can be realized in such a simple model. We find that the dens…
Motivated by the recent experiments that reported signatures of many-body localization of ultracold atoms in optical lattices [M. Schreiber {\it et al.}, Science {\bf 349}, 842 (2015)], we study dynamics of highly excited states in the strongly disordered Hubbard model in one dimension. Owing to the $SU(2)$ spin symmetry, spin degrees of freedom form a delocalized thermal bath with a narrow bandwidth. The spin bath mediates slow particle transport, eventually leading to delocalization of particles. The particle hopping rate is exponentially small in $t/W$ ($t$, $W$ being hopping and disorder s…
