We investigate an imbalanced mixture composed of two-color fermions and scalar bosons in the hard-core limit, considering repulsive and attractive interspecies and intraspecies interactions. The interplay between commensurability, repulsive interactions and imbalance generates three insulating phases: a mixed Mott state and two spin-selective insulators characterized by the commensurability relations $ρ_B+ρ^{\uparrow,(\downarrow)}_F=1$. For an attractive coupling between fermions and bosons, we found the relations $ρ_B-ρ^{\uparrow,(\downarrow)}_F=0$ for the spin-selective insulators. State-of-the-art cold-atoms setups constitute ideal platforms to implement these unveiled insulating states and verify their commensurability relations.
The standard mean-field theory for the Mott insulator-superfluid phase transition is not sufficient to describe the Mott insulator-paired superfluid phase transition. Therefore, by restricting the two-species Bose-Hubbard Hamiltonian to the subspace of paired particles, and using perturbation theory, here we derive an analytic mean-field expression for the Mott insulator-paired superfluid transition boundary.
We study topological properties of the Bose-Hubbard model with repulsive interactions in a one-dimensional optical superlattice. We find that the Mott insulator states of the single-component (two-component) Bose-Hubbard model under fractional fillings are topological insulators characterized by a nonzero charge (or spin) Chern number with nontrivial edge states. For ultracold atomic experiments, we show that the topological Chern number can be detected through measuring the density profiles of the bosonic atoms in a harmonic trap.
Quantum criticality near a tricritical point (TCP) is studied in the two-component Bose-Hubbard model on square lattices. The existence of quantum TCP on a boundary of superfluid-insulator transition is confirmed by quantum Monte Carlo simulations. Moreover, we analytically derive the quantum tricritical behaviors on the basis of an effective field theory. We find two significant features of the quantum tricriticality, that are the chemical potential dependence of the superfluid transition temperature and a strong density fluctuation. We suggest that these features are directly observable in e…
We perform a numeric study (Worm algorithm Monte Carlo simulations) of ultracold two-component bosons in two-dimensional optical lattices. We study how the Mott insulator to superfluid transition is affected by the presence of a second superfluid bosonic species. We find that, at fixed interspecies interaction, the upper and lower boundaries of the Mott lobe are differently modified. The lower boundary is strongly renormalized even for relatively low filling factor of the second component and moderate (interspecies) interaction. The upper boundary, instead, is affected only for large enough fi…
We investigate the formation of discrete breathers (DBs) and the dynamics of the mixture of two-species Bose-Einstein condensates (BECs) in open boundary optical lattices using the discrete nonlinear Schrödinger equations. The results show that the coupling of intra- and interspecies interaction can lead to the existence of pure single-species DBs and symbiotic DBs (i.e., two-species DBs). Furthermore, we find that there is a selective distillation phenomenon in the dynamics of the mixture of two-species BECs. One can selectively distil one species from the mixture of two-species BECs and can …
We study the two-dimensional weakly repulsive Bose gas at zero temperature in the presence of correlated disorder. Using large-scale simulations, we show that the low-energy Bogoliubov cumulative density of states remains quadratic up to a critical disorder strength, beyond which a power law with disorder-dependent exponent $β<2$ sets in. We associate this threshold behavior with the transition from superfluid to Bose glass, and compare the resulting mean-field phase diagram with scaling laws and the Thomas-Fermi percolation threshold of the mean-field density profile.
We study the quantum phase transition between the superfluid and the Mott insulator in the one-dimensional (1D) Bose-Hubbard model. Using the time-evolving block decimation method, we numerically calculate the tunneling splitting of two macroscopically distinct states with different winding numbers. From the scaling of the tunneling splitting with respect to the system size, we determine the critical point of the superfluid to Mott insulator transition for arbitrary integer filling factors. We find that the critical values versus the filling factor in 1D, 2D, and 3D are well approximated by a …
By means of the method of the effective potential, the phase transitions from the Mott insulating state to either the atomic or the dimer superfluid state in the three-body constrained attractive Bose lattice gas are analyzed. Due to the appearance of the Feshbach resonance coupling between the two kinds of order parameters in the derived effective potential function, it is found that the continuous Mott insulator-to-superfluid transitions can be preempted by first-order ones. Since the employed approach can provide accurate predictions of phase boundaries in the strong coupling limit, where t…
An iterative scheme based on the kernel polynomial method is devised for the efficient computation of the one-body density matrix of weakly interacting Bose gases within Bogoliubov theory. This scheme is used to analyze the coherence properties of disordered bosons in one and two dimensions. In the one-dimensional geometry, we examine the quantum phase transition between superfluid and Bose glass at weak interactions, and we recover the scaling of the phase boundary that was characterized using a direct spectral approach by Fontanesi et al. [Phys. Rev. A 81, 053603 (2010)]. The kernel polynomi…
We theoretically study dynamical formation of a quantum droplet in a two-component Bose-Hubbard system with an external trap potential. Specifically, the superfluid in the central region surrounded by the Mott insulator with double filling forms a quantum droplet, which is self-bound thanks to the discontinuous nature of the quantum phase transition between the two phases. We show how to induce the characteristic behavior of the droplet through the control of the trap potential by using the time-dependent Gutzwiller simulations in a two-dimensional system. The static and dynamical properties o…
We study a three-component fermionic fluid in an optical lattice in a regime of intermediate-to- strong interactions allowing for Raman processes connecting the different components, similar to those used to create artificial gauge fields (AGF). Using Dynamical Mean-Field Theory we show that the combined effect of interactions and AGFs induces a variety of anomalous phases in which different components of the fermionic fluid display qualitative differences, i.e., the physics is flavor-selective. Remarkably, the different components can display huge differences in the correlation effects, measu…
We study the superfluid-Mott insulator (SF-MI) transition in an one-dimensional optical lattice system, and employ the Bose-Hubbard model in two dimension with a combined potential of an optical lattice in one direction and a confining harmonic trap in the other direction, which we refer to as the pseudo one-dimension Bose-Hubbard model. There some excited states with respect to the harmonic trap are considered. The Mott lobes shrink in the $μ$ and $J$ directions of the $μ$-$J$ phase diagram. The shrinkage occurs because the interactions involving the excited states become weaker than that bet…
We report on a novel structural Superfluid-Mott Insulator (SF-MI) quantum phase transition for an interacting one-dimensional Bose gas within permeable multi-rod lattices, where the rod lengths are varied from zero to the lattice period length. We use the ab-initio diffusion Monte Carlo method to calculate the static structure factor, the insulation gap, and the Luttinger parameter, which we use to determine if the gas is a superfluid or a Mott insulator. For the Bose gas within a square Kronig-Penney (KP) potential, where barrier and well widths are equal, the SF-MI coexistence curve shows th…
Motivated by the experimental realization of synthetic spin-orbit coupling for ultracold atoms, we investigate the phase diagram of the Bose Hubbard model in a non-abelian gauge field in two dimensions. Using a strong coupling expansion in the combined presence of spin-orbit coupling and tunable interactions, we find a variety of interesting magnetic Hamiltonians in the Mott insulator (MI), which support magnetic textures such as spin spirals and vortex and Skyrmion crystals. An inhomogeneous mean field treatment shows that the superfluid (SF) phases inherit these exotic magnetic orders from t…
We analyze the momentum distribution function and its artificial-gauge-field dependence for the Mott insulator phases of the Hofstadter-Bose-Hubbard model. By benchmarking the results of the random-phase approximation (RPA) approach against those of the strong-coupling expansion (SCE) for the Landau and symmetric gauges, we find pronounced corrections to the former results in two dimensions.
Dissipation is ubiquitous in nature and plays a crucial role in quantum systems such as causing decoherence of quantum states. Recently, much attention has been paid to an intriguing possibility of dissipation as an efficient tool for preparation and manipulation of quantum states. Here we report the realization of successful demonstration of a novel role of dissipation in a quantum phase transition using cold atoms. We realize an engineered dissipative Bose-Hubbard system by introducing a controllable strength of two-body inelastic collision via photo-association for ultracold bosons in a thr…
In this paper, we studied a generalized Bose-Hubbard model on a checkerboard lattice with topologically nontrivial flat-band. We used mean-field method to decouple the model Hamiltonian and obtained phase diagram by Landau theory of second-order phase transition. We further calculate the energy gap and the dispersion of quasi-particle or quasi-hole in Mott insulator state and found that in strong interaction limit the quasi-particles or the quasi-holes also have flat bands.
We study the quantum phase transition from the superfluid to the Mott insulator state in two and three dimensional Bose-Einstein condensate (BEC) with optical lattices using Bose-Hubbard Hamiltonian within the Generalized Hatree-Fock-Bogoliubov (GHFB) approximation. The behavior of the depletion and the anomalous fraction has been investigated in the Mott insulator phase. We found that at T = 0, these quantities become significant in two and three dimensions. It is shown also that the dimensionality of the lattice enhances the anomalous density.
We study the thermodynamics near the generic (density-driven) superfluid--Mott-insulator transition in the three-dimensional Bose-Hubbard model using the nonperturbative renormalization-group approach. At low energy the physics is controlled by the Gaussian fixed point and becomes universal. Thermodynamic quantities can then be expressed in terms of the universal scaling functions of the dilute Bose gas universality class while the microscopic physics enters only {\it via} two nonuniversal parameters, namely the effective mass $m^*$ and the "scattering length" $a^*$ of the elementary excitatio…
We model the dynamics of two species of bosonic atoms trapped in an optical lattice within the Mott regime by mapping the system onto a spin model. A field gradient breaks the cloud into two domains. We study how the domain wall evolves under adiabatic and diabatic changes of this gradient. We determine the timescales for adiabaticity, and study how temperature evolves for slow ramps. We show that after large, sudden changes of the field gradient, the system does not equilibrate on typical experimental timescales. We find interesting spin dynamics even when the initial temperature is large com…
We consider a square optical lattice in two dimensions and study the effects of both the strength and symmetry of spin-orbit-coupling (SOC) and Zeeman field on the ground-state, i.e., Mott insulator (MI) and superfluid (SF), phases and phase diagram, i.e., MI-SF phase transition boundary, of the two-component Bose-Hubbard model. In particular, based on a variational Gutzwiller ansatz, our numerical calculations show that the spin-orbit coupled SF phase is a nonuniform (twisted) one with its phase (but not the magnitude) of the order parameter modulating from site to site. Fully analytical insi…
We investigate experimentally and theoretically the dynamical properties of a Mott insulator in decoupled one-dimensional chains. Using a theoretical analysis of the Bragg excitation scheme we show that the spectrum of inter-band transitions holds information on the single-particle Green's function of the insulator. In particular the existence of particle-hole coherence due to quantum fluctuations in the Mott state is clearly seen in the Bragg spectra and quantified. Finally we propose a scheme to directly measure the full, momentum resolved spectral function as obtained in angle-resolved phot…
The superfluid to Mott insulator transition and the superradiant transition are textbook examples for quantum phase transition and coherent quantum optics, respectively. Recent experiments in ETH and Hamburg succeeded in loading degenerate bosonic atomic gases in optical lattices inside a cavity, which enables the first experimental study of the interplay between these two transitions. In this letter we present the theoretical phase diagram for the ETH experimental setup, and determine the phase boundaries and the orders of the phase transitions between the normal superfluid phase, the superfl…
We investigate the nature of the superfluid-insulator quantum phase transition driven by disorder for non-interacting ultracold atoms on one-dimensional lattices. We consider two different cases: Anderson-type disorder, with local energies randomly distributed, and pseudo-disorder due to a potential incommensurate with the lattice, which is usually called the Aubry-André model. A scaling analysis of numerical data for the superfluid fraction for different lattice sizes allows us to determine quantum critical exponents characterizing the disorder-driven superfluid-insulator transition. We also …
We study the fully gapped chiral Mott insulator (CMI) of frustrated Bose-Hubbard models on ladders and two-dimensional lattices by perturbative strong-coupling analysis and density matrix renormalization group (DMRG). First we show the existence of a low-lying exciton state on all geometries carrying the correct quantum numbers responsible for the condensation of excitons and formation of the CMI in the intermediate interaction regime. Then we perform systematic DMRG simulations on several two-leg ladder systems with $π$-flux and carefully characterize the two quantum phase transitions. We dis…
We investigate the momentum-dependent transport of 1D quasi-condensates in quasiperiodic optical lattices. We observe a sharp crossover from a weakly dissipative regime to a strongly unstable one at a disorder-dependent critical momentum. In the limit of non-disordered lattices the observations indicate a contribution of quantum phase slips to the dissipation. We identify a set of critical disorder and interaction strengths for which such critical momentum vanishes, separating a fluid regime from an insulating one. We relate our observation to the predicted zero-temperature superfluid-Bose gla…
We study the extended Bose-Hubbard model on the square lattice at half filling as a function of next-nearest neighbor hopping amplitude and interaction strength. To variationally map out the phase diagram of this model, we develop a two-parameter family of wave-functions based on the parton construction which can describe both topological and broken symmetry phases on equal footing. In addition, our wave-functions resolve long standing issues with more conventional short-range Jastrow wave-functions. Using this variational ansatz, we show that a spontaneous time-reversal symmetry breaking frac…
We introduce a detector that selectively probes the phononic excitations of a cold Bose gas. The detector is composed of a single impurity atom confined by a double-well potential, where the two lowest eigenstates of the impurity form an effective probe qubit that is coupled to the phonons via density-density interactions with the bosons. The system is analogous to a two-level atom coupled to photons of the radiation field. We demonstrate that tracking the evolution of the qubit populations allows probing both thermal and coherent excitations in targeted phonon modes. The targeted modes are se…
We study ground-state phase diagrams and excitation spectra of Bose-Bose mixtures in an optical lattice by applying the Gutzwiller approximation to the two-component Bose-Hubbard model. A case of equal hoppings and equal intra-component interactions for both components is considered. Due to the existence of inter-component interaction, there appear several quantum phases, such as the superfluid, paired superfluid, and counterflow superfluid phases. We find that the transition from superfluid (SF) to Mott insulator (MI) with even filling factors can be of the first order for a wide range of the…
Structure and Dynamics of Bose Polarons across the Mott-Insulator to Superfluid Transition
Institute of Science and Technology Austria (ISTA)（奥地利科学与技术研究院）；Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento（特伦托大学物理系、意大利国家研究委员会光学研究所皮塔耶夫斯基玻色-爱因斯坦凝聚中心）；Trento Institute for Fundamental Physics and Applications, INFN（特伦托基础物理与应用研究所，意大利国家核物理研究所）；Department of Physics and Astronomy, Aarhus University（奥胡斯大学物理与天文学系）
We investigate the zero-temperature phase diagram of interacting Bose gases in the presence of a simple cubic optical lattice, going beyond the regime where the mapping to the single-band Bose-Hubbard model is reliable. Our computational approach is a new hybrid quantum Monte Carlo method which combines algorithms used to simulate homogeneous quantum fluids in continuous space with those used for discrete lattice models of strongly correlated systems. We determine the critical interaction strength and optical lattice intensity where the superfluid-to-insulator transition takes place, consideri…
Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the "fully frustrated" Bose-Hubbard (FFBH) model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a two-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical XY model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop curre…
We apply the theory of inhomogeneous Kibble-Zurek mechanism to understand quench dynamics from the Mott insulator to the superfluid in a cold Bose gases confined in both a two-dimensional optical lattice and a harmonic trap. The local quench time and the freeze-out region associated with the nonadiabatic transition take a nontrivial positional dependence due to the Mott-lobe structure of the ground state phase diagram of the Bose-Hubbard model. We demonstrate that the quench dynamics through the time-dependent Gutzwiller simulations, revealing inhomogeneous properties of the growth of the supe…
We study the expansion of bosonic Mott insulators in the presence of an optical lattice after switching off a confining potential. We use the Gutzwiller mean-field approximation and consider two different setups. In the first one, the expansion is restricted to one direction. We show that this leads to the emergence of two condensates with well defined momenta, and argue that such a construct can be used to create atom lasers in optical lattices. In the second setup, we study Mott insulators that are allowed to expand in all directions in the lattice. In this case, a simple condensate is seen …
We investigate the interaction-induced superfluid-to-Mott insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings $n=1$, $n=2$, and $n=3$ by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermion…
We propose a new class of tight-binding systems of interacting bosons with a flat band, which are exactly solvable in the sense that one can explicitly write down the unique ground state. The ground state is expressed in terms of local creation operators, and apparently resembles that of a Mott insulator. Based on an exact representation in terms of a classical loop-gas model, we conjecture that the ground state may exhibit quasi Bose-Einstein condensation (BEC) or genuine BEC in dimensions two and three or higher, respectively, still keeping Mott insulator-like character. Our Monte Carlo simu…
We investigate the superfluid-insulator quantum phase transition in a disordered 1D Bose gas in the mean field limit, by studying the probability distribution of the density. The superfluid phase is characterized by a vanishing probability to have zero density, whereas a nonzero probability marks the insulator phase. This relation is derived analytically, and confirmed by a numerical study. This fragmentation criterion is particularly suited for detecting the phase transition in experiments. When a harmonic trap is included, the transition to the insulating phase can be extracted from the stat…
We perform an extensive numerical study on the breathing dynamics of a few-body Bose polaron setup in a one-dimensional species-selective harmonic trap. The dynamics is triggered by a quench of the impurity trap. The excitation of the background majority atoms is mediated via the majority-impurity interaction. The breathing spectrum is obtained for different numbers of majority particles, several values of the majority-component interaction strengths and trap ratios. It is further compared to the breathing spectrum of a particle-balanced few-body Bose-Bose mixture. In particular, for equal pos…
We study the zero temperature phase diagram of the disordered spin-1 Bose-Hubbard model in a 2-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 …
We propose to use the method introduced by Volchkov et al., based on state dependent disordered ultracold bosons, to address the critical state at the mobility edge of the Anderson localization transition, and to observe its intriguing multifractal structure. An optimally designed external radio frequency pulse can be applied to generate transitions to eigenstates in a narrow energy window close to the mobility edge, where critical scaling and multifractality emerge. Two-photon laser scanning microscopy will be used to address individual localized states even close to the transition. The proje…
We theoretically investigate spin transfer between a system of quasiequilibrated Bose-Einstein condensed magnons in an insulator in direct contact with a conductor. While charge transfer is prohibited across the interface, spin transport arises from the exchange coupling between insulator and conductor spins. In normal insulator phase, spin transport is governed solely by the presence of thermal and spin-diffusive gradients; the presence of Bose-Einstein condensation (BEC), meanwhile, gives rise to a temperature-independent condensate spin current. Depending on the thermodynamic bias of the sy…
We study two models realized by two-component Fermi gases loaded in optical lattices. We clarify that multi-band effects inevitably caused by the optical lattices generate a rich structure, when the systems crossover from the region of weakly bound molecular bosons to the region of strongly bound atomic bosons. Here the crossover can be controlled by attractive fermion interaction. One of the present models is a case with attractive fermion interaction, where an insulator-superfluid transition takes place. The transition is characterized as the transition between a band insulator and a Bose-Ei…
In this work, we study a one-dimensional model of interacting bosons coupled to a dynamical $\mathbb{Z}_2$ field, the $\mathbb{Z}_2$ Bose-Hubbard model, and analyze the interplay between spontaneous symmetry breaking and topological symmetry protection. In a previous work, we showed how this model exhibits a spontaneous breaking of the translational symmetry through a bosonic Peierls transition. Here we find how, at half filling, the resulting phase also displays topological features that coexist with the presence of long-range order and yields a topological bond order wave. Using both analyti…
A spin-wave approach of the zero temperature superfluid-insulator transition for two-dimensional hard-core bosons in a random potential $μ=\pm$ W is developed. While at the classical level there is no intervening phase between the Bose-condensed superfluid (SF) and the gapped disordered insulator, the introduction of quantum fluctuations leads to a much richer physics. Upon increasing the disorder strength W, the Bose-condensed fraction disappears first, before the SF. Then a gapless Bose-glass phase emerges over a finite region until the insulator appears. Furthermore, in the strongly disorde…
We use the Gutzwiller ansatz and analyze the phase diagram of the extended Bose-Hubbard Hamiltonian with on-site (U) and nearest-neighbor (V) repulsions. For $d$-dimensional hypercubic lattices, when 2dV < U, it is well-known that the ground state alternates between the charge-density-wave (CDW) and Mott insulators, and the supersolid (SS) phase occupies small regions around the CDW insulators. However, when 2dV > U, in this paper, we show that the ground state has only CDW insulators, and more importantly, the SS phase occupies a much larger region in the phase diagram, existing up to very la…
We report on results of Quantum Monte Carlo simulations for bosons in a two dimensional quasi-periodic optical lattice. We study the ground state phase diagram at unity filling and confirm the existence of three phases: superfluid, Mott insulator, and Bose glass. At lower interaction strength, we find that sizable disorder strength is needed in order to destroy superfluidity in favor of the Bose glass. On the other hand, at large enough interaction superfluidity is completely destroyed in favor of the Mott insulator (at lower disorder strength) or the Bose glass (at larger disorder strength). …
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…
Motivated by experiments on Josephson junction arrays in a magnetic field and ultracold interacting atoms in an optical lattice in the presence of synthetic orbital magnetic fields, we study the "fully frustrated" Bose-Hubbard model and quantum XY model with half a flux quantum per lattice plaquette. Using Monte Carlo simulations and the density matrix renormalization group (DMRG) method, we show that the phase diagram of such kinetically frustrated bosons displays three phases on a two-leg ladder: a weakly interacting chiral superfluid phase with staggered loop currents which spontaneously br…
To analyze the ground-state phase diagram of Bose-Bose mixtures loaded into $d$-dimensional hypercubic optical lattices, we perform a strong-coupling power-series expansion in the kinetic energy term (plus a scaling analysis) for the two-species Bose-Hubbard model with onsite boson-boson interactions. We consider both repulsive and attractive interspecies interaction, and obtain an analytical expression for the phase boundary between the incompressible Mott insulator and the compressible superfluid phase up to third order in the hoppings. In particular, we find a re-entrant quantum phase trans…
We investigate the quantum phase diagram of Bose-Fermi mixtures of ultracold dipolar particles trapped in one-dimensional optical lattices in the thermodynamic limit. With the presence of nearest-neighbor (N.N.) interactions, a long-ranged ordered crystalline phase (Bose-Fermi solid) is found stabilized between a Mott insulator of bosons and a band-insulator of fermions in the limit of weak inter-site tunneling ($J$). When $J$ is increased, such a Bose-Fermi solid can be quantum melted into a Bose-Fermi liquid through either a two-stage or a three-stage transition, depending on whether the cry…
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 superfluid to Anderson insulator transition of strongly repulsive Bose gas in a one dimensional incommensurate optical lattice. In the hard core limit, the Bose-Fermi mapping allows us to deal with the system exactly by using the exact numerical method. Based on the Aubry-André model, we exploit the phase transition of the hard core boson system from superfluid phase with all the single particle states being extended to the Bose glass phase with all the single particle states being Anderson localized as the strength of the incommensurate potential increasing relative to the amplitude …
The entanglement spectrum provides crucial information about correlated quantum systems. We show that the study of the block-like nature of the reduced density matrix in number sectors and the partition dependence of the spectrum in finite systems leads to interesting unexpected insights, which we illustrate for the case of a 1D extended Hubbard model. We show that block symmetry provides an intuitive understanding of the spectral double degeneracy of the Haldane-insulator, revealing as well partial double degeneracy for the Mott-insulator. Moreover, surprisingly, the partition dependence of t…
In order to identify possible experimental signatures of the superfluid to Mott-insulator quantum phase transition we calculate the charge structure factor $S(k,ω)$ for the one-dimensional Bose-Hubbard model using the dynamical density-matrix renormalisation group (DDMRG) technique. Particularly we analyse the behaviour of $S(k, ω)$ by varying---at zero temperature---the Coulomb interaction strength within the first Mott lobe. For strong interactions, in the Mott-insulator phase, we demonstrate that the DDMRG results are well reproduced by a strong-coupling expansion, just as the quasi-particl…
