We calculate the excitation spectra of a spin-polarized Hubbard chain away from half-filling, using a high-precision momentum-resolved time-dependent Density Matrix Renormalization Group method. Focusing on the U<0 case, we present in some detail the single-fermion, pair, density and spin spectra, and discuss how spin-charge separation is altered for this system. The pair spectra show a quasi-condensate at a nonzero momentum proportional to the polarization, as expected for this Fulde-Ferrel-Larkin-Ovchinnikov-like superfluid.
We study the Luttinger-liquid parameter $K_ρ$ of the Hubbard chain and the Hubbard ladder models by the ordinary perturbation method combined with the Luttinger-liquid relation. According to the Luttinger-liquid relation, the critical exponent $K_ρ$ is related to the charge susceptibility $χ_c$ and the Drude weight D by $ K\sbρ={1/2}(πχ_c D)^{1/2}$. By calculating these quantities with the perturbation method, we obtain $K_ρ$ at the first-order analytically and up to the second-order numerically. We compare these results with results of the Bethe ansatz for the Hubbard chain and that of the nu…
Using the first-order series expansion of the function G(k;mu), in powers of mu' = mu - U/2, pertaining to the insulating ground state of a single-band Hubbard Hamiltonian at half-filling, Kokalj and Prelovsek have in a recent paper [Eur. Phys. J. B 63, 431 (2008), arXiv:arXiv:0709.0263] reported breakdown of the Luttinger theorem for the specific case where the lattice on which the Hubbard Hamiltonian is defined is a two-dimensional triangular lattice, for which the ground state is not invariant under particle-hole transformation. Here G(k;mu) is the single-particle Green function G(k;e) eval…
We give the first rigorous (non perturbative) proof of Luttinger liquid behavior in the one dimensional Hubbard model, for small repulsive interaction and values of the density different from half filling. The analysis is based on the combination of multiscale analysis with Ward identities bases on a hidden and approximate local chiral gauge invariance. No use is done of exact solutions or special integrability properties of the Hubbard model, and the results can be in fact easily generalized to include non local interactions, magnetic fields or interaction with external potentials
We investigate the momentum distribution function near the Mott-Hubbard transition in the one-dimensional t1-t2 Hubbard model (the zig-zag Hubbard chain), with the density-matrix renormalization-group technique. We show that for strong interactions the Mott-Hubbard transition occurs between the metallic-phase and an insulating dimerized phase with incommensurate spin excitations, suggesting a decoupling of magnetic and charge excitations not present in weak coupling. We illustrate the signatures for the Mott-Hubbard transition and the commensurate-incommensurate transition in the insulating sp…
The electronic system of the 1D Hubbard model is not stable due to Peierls instability; the correlations are strong even for the weak Coulomb interaction. The resulting strongly correlated state without Landau quisi--particle excitations is known as the Luttinger liquid. Critical exponents of a power--law dependence of correlation functions at low energies differ substantially for the Luttinger and Fermi liquids. In this paper we evaluate two critical exponents that define non--trivial behavior of the density of electronic states at low frequences and the momentum distribution of the occupatio…
The known analytical properties of the Green's function and self-energy rule out an ambiguity of the self-energy. The noninteracting Green's functions obtained by Kozik et al. in arXiv:1407.5687 likely have pathological properties.
The frequency-moment expansion method is developed to analyze the validity of the Luttinger sum rule within the Mott-Hubbard insulator, as represented by the generalized Hubbard model at half filling and large $U$. For the particular case of the Hubbard model with nearest-neighbor hopping on a triangular lattice lacking the particle-hole symmetry results reveal substantial violation of the sum rule.
The validity of the Luttinger sum rule is investigated within the prototype tight-binding model of interacting fermions in one dimension, i.e., the t-V model including the next-nearest neighbor hopping t' in order to break the particle-hole symmetry. Scaling analysis of finite-system results at half-filling reveals evident breakdown of the sum rule in the regime of large gap at V >> t, while the sum rule appears to recover together with vanishing of the Mott-Hubbard gap.
We study the one-dimensional extended Hubbard model with alternating size of the hopping integrals using the density-matrix renormalization group method. We calculate the spin gap, the Tomonaga-Luttinger parameter, and the charge-density-wave order parameter for various dimerizations, interaction strengths, and band fillings. At half band-filling the spin and charge excitations are gapped but these gaps disappear for infinitesimal hole doping. At quarter filling, the Umklapp scattering in the half-filled lower Peierls band generates a gap for the charge excitations but the gapless spin excitat…
We show that a particular class of variational wave functions reproduces the low-energy properties of the Hubbard model in one dimension. Our approach generalizes to finite on-site Coulomb repulsion the fully-projected wave function proposed by Hellberg and Mele [Phys. Rev. Lett. {\bf 67}, 2080 (1991)] for describing the Luttinger-liquid behavior of the doped $t{-}J$ model. Within our approach, the long-range Jastrow factor emerges from a careful minimization of the energy, without assuming any parametric form for the long-distance tail. Specifically, in the conducting phase of the Hubbard mod…
We study the 1D extended Hubbard model with a weak repulsive short-range interaction in the non-half-filled band case, using non-perturbative Renormalization Group methods and Ward Identities. At the critical temperature, T = 0, the response functions have anomalous power-law decay with multiplicative logarithmic corrections. The critical exponents, the susceptibility and the Drude weight verify the universal Luttinger liquid relations. Borel summability and (a weak form of) Spin-Charge separation is established.
We present an extensive numerical study of the Hubbard model on the doped AB$_2$ chain, both in the weak coupling and the infinite-U limit. Due to the special unit cell topology, this system displays a rich variety of phases as function of hole doping ($δ$) away from half-filling. Near half-filling, spiral states develop in the weak coupling regime, while Nagaoka itinerant ferromagnetism is observed in the infinite-U limit. For higher doping the system phase-separates before reaching a Mott insulating phase of short-range RVB states at $δ=1/3$. Moreover, for $δ>1/3$ we observe a crossover, whi…
We study a two-component Fermi system with attractive interactions and different populations of the two species in a cubic lattice. For an intermediate coupling we find a uniformly polarized superfluid which is stable down to very low temperatures. The momentum distribution of this phase closely resembles that of the Sarma phase, characterized by two Fermi surfaces. This phase is shown to be stabilized by a potential energy gain, as in a BCS superfluid, in contrast to the unpolarized BEC which is stabilized by kinetic energy. We present general arguments suggesting that preformed pairs in the …
To explore superfluidity in flat-band systems, we consider a Bose-Hubbard model on a cross-linked ladder with $π$ flux, which has a flat band with a gap between the other band for noninteracting particles, where we study the effect of the on-site repulsion nonperturbatively. For low densities, we find exact degenerate ground states, each of which is a Wigner solid with nonoverlapping Wannier states on the flat band. At higher densities, the many-body system, when projected onto the lower flat band, can be mapped to a spin-chain model. This mapping enables us to reveal the existence of a Tomona…
The correlation functions of one-dimensional Hubbard model in the presence of external magnetic field was investigated through the conformal field technique. The long distance behaviour of the correlation functions and their critical exponents for the model in the presence of a magnetic field are established by solving the dressed charge matrix equations and setting the number of occupancies to one, as an alternative to the usual zero often used by authors in literatures. Our result shows the critical exponents of the correlation function grows monotonically with magnetic field and reduces to …
Strongly coupled field theories with gravity duals can be placed at finite density in two ways: electric field flux emanating from behind a horizon, or bulk charged fields outside of the horizon that explicitly source the density. We discuss field-theoretical observables that are sensitive to this distinction. If the charged fields are fermionic, we discuss a modified Luttinger's theorem that holds for holographic systems, in which the sum of boundary theory Fermi surfaces counts only the charge outside of the horizon. If the charged fields are bosonic, we show that the the resulting superflui…
We construct and apply an exchange-correlation functional for the one-dimensional Hubbard model. This functional has built into it the Luttinger-liquid and Mott-insulator correlations, present in the Hubbard model, in the same way in which the usual {\it ab initio} local-density approximation (LDA) has built into it the Fermi-liquid correlations present in the electron gas. An accurate expression for the exchange-correlation energy of the homogeneous Hubbard model, based on the Bethe Ansatz (BA), is given and the resulting LDA functional is applied to a variety of inhomogeneous Hubbard models.…
We use microscopic Bogoliubov-de Gennes formalism to explore the ground-state phase diagram of the single-band attractive Hofstadter-Hubbard model on a square lattice. We show that the interplay between the Hofstadter butterfly and superfluidity breaks spatial symmetry, and gives rise to stripe-ordered superfluid and supersolid phases in large parameter spaces. We also discuss the effects of a trapping potential and comment on the viability of observing stripe-ordered phases with cold Fermi gases.
We present a Monte Carlo study of the Bose-glass to superfluid transition in the three-dimensional Bose-Hubbard model. Simulations are performed on the classical (3 + 1) dimensional link-current representation using the geometrical worm algorithm. Finite-size scaling analysis (on lattices as large as 16x16x16x512 sites) of the superfluid stiffness and the compressibility is consistent with a value of the dynamical critical exponent z = 3, in agreement with existing scaling and renormalization group arguments that z = d. We find also a value of $ν= 0.70(12)$ for the correlation length exponent,…
The Luttinger-Ward functional $Φ[\mathbf{G}]$, which expresses the thermodynamic grand potential in terms of the interacting single-particle Green's function $\mathbf{G}$, is found to be ill-defined for fermionic models with the Hubbard on-site interaction. In particular, we show that the self-energy $\mathbfΣ[\mathbf{G}] \propto δΦ[\mathbf{G}]/δ\mathbf{G}$ is not a single-valued functional of $\mathbf{G}$: in addition to the physical solution for $\mathbfΣ[\mathbf{G}]$, there exists at least one qualitatively distinct unphysical branch. This result is demonstrated for several models: the Hubb…
We study fermionic superfluidity in strongly anisotropic optical lattices with attractive interactions utilizing the cluster DMFT method, and focusing in particular on the role of non-local quantum fluctuations. We show that non-local quantum fluctuations impact the BCS superfluid transition dramatically. Moreover, we show that exotic superfluid states with delicate order parameter structure, such as the Fulde-Ferrell-Larkin-Ovchinnikov phase driven by spin population imbalance, can emerge even in the presence of such strong fluctuations.
Antiferromagnetic, Mott insulator, d-wave and gossamer superfluid phases are calculated for 2D square lattices from the extended Hubbard (t-J-U) model using the Gutzwiller projection method and renormalized mean field theory. Phase separation between antiferromagnetic and d-wave superfluid phases is found near half filling when the on-site repulsion exceeds $U\ga7.3t$, and coincides with a first order transition in the double occupancy. Phase separation is thus predicted for 2D optical lattices with ultracold Fermi atoms whereas it is inhibited in cuprates by Coulomb frustration which instead …
The proof of the Luttinger theorem, which was originally given for a normal Fermi liquid with equal spin populations formally described by the exact many-body theory at zero temperature, is here extended to an approximate theory given in terms of a "conserving" approximation also with spin imbalanced populations. The need for this extended proof, whose underlying assumptions are here spelled out in detail, stems from the recent interest in superfluid trapped Fermi atoms with attractive inter-particle interaction, for which the difference between two spin populations can be made large enough th…
We investigate the superfluid properties of d-wave pairing symmetry within the Extended Hubbard Model (EHM) in a magnetic field. We analyze the temperature and magnetic field dependencies of the order parameter. We find that in the two-dimensional case, the spatially homogeneous spin polarized superfluidity ($SC(P\neq0)$) is stable in the weak coupling limit, at T=0, as opposed to the s-wave pairing symmetry case in 2D. We construct the ground state phase diagrams both for fixed chemical potential ($μ$) and electron concentration ($n$). Furthermore, we obtain the temperature vs. magnetic field…
We study the zero temperature mean-field phase diagram of the Bose-Hubbard model in the presence of local coupling between the bosons and an external bath. We consider a coupling that conserves the on-site occupation number, preserving the robustness of the Mott and superfluid phases. We show that the coupling to the bath renormalizes the chemical potential and the interaction between the bosons and reduces the size of the superfluid regions between the insulating lobes. For strong enough coupling, a finite value of hopping is required to obtain superfluidity around the degeneracy points where…
Despite the multi-band spectrum of the widely-known Hofstadter butterfly, it turns out that the pairing correlations of the time-reversal-symmetric Hofstadter-Hubbard model are well-described by a single order parameter that is uniform in real space. By exploiting a BCS mean-field theory for the nearly-flat butterfly-bands regime of low magnetic-flux limit, here we reveal a number of unusual superfluid properties both in the ground state and at finite temperatures. Our thorough analysis includes but is not limited to the order parameter, condensate and superfluid fractions, and the critical BC…
We present a novel treatment of finite temperature properties of the one-dimensional Hubbard model. Our approach is based on a Trotter-Suzuki mapping utilizing Shastry's classical model and a subsequent investigation of the quantum transfer matrix. We derive non-linear integral equations for three auxiliary functions which have a clear physical interpretation of elementary excitations of spin type and charge excitations in lower and upper Hubbard bands. This allows for a transparent analytical study of certain limiting cases as well as for precise numerical investigations. We present data for …
We analyze a model of two-leg Hubbard ladders weakly coupled by interladder tunneling. At half filling a semimetallic state with small Fermi pockets is induced beyond a threshold tunneling strength. The sign changes in the single electron Green's function relevant for the Luttinger Sum Rule now take place at surfaces with both zeroes and infinities with important consequences for the interpretation of ARPES experiments. Residual interactions between electron and hole-like quasi-particles cause a transition to long range order at low temperatures. The theory can be extended to small doping lead…
In addition to the conventional contribution that is directly controlled by the single-particle energy spectrum, the superfluid phase stiffness of a two-component Fermi gas has a geometric contribution that is governed by the quantum metric of the honeycomb's band structure. Here, we take both contributions into account, and construct phase diagrams for the critical superfluid transition temperature as a function of the chemical potential, particle filling, onsite interaction and next-nearest-neighbor hopping. Our theoretical approach is based on a self-consistent solution of the BCS mean-fiel…
We study the superfluid-insulator transition in Bose-Hubbard models in one-, two-, and three-dimensional cubic lattices by means of a recently proposed variational wave function. In one dimension, the variational results agree with the expected Berezinskii-Kosterlitz-Thouless scenario of the interaction-driven Mott transition. In two and three dimensions, we find evidences that, across the transition,most of the spectral weight is concentrated at high energies, suggestive of pre-formed Mott-Hubbard side-bands. This result is compatible with the experimental data by Stoferle et al. [Phys. Rev. …
We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we repro…
We present a numerical approach to study the coherent transport of Cooper pairs through a Hubbard chain, and study the role of the contacts in achieving perfect Andreev reflection. We calculate the pair transport using the Density Matrix Renormalization Group by measuring the response of the system to quantum pair fields with complex phases on the two ends of an open system. This approach gives an effective superfluid weight which is in close agreement with the Bethe Ansatz results for the superfluid weight for closed Hubbard rings.
We consider a Fermi gas that is loaded onto a square optical lattice and subjected to a perpendicular artificial magnetic field, and determine its superfluid transition boundary by adopting a BCS-like mean-field approach in momentum space. The multi-band structure of the single-particle Hofstadter spectrum is taken explicitly into account while deriving a generalized pairing equation. We present the numerical solutions as functions of the artificial magnetic flux, interaction strength, Zeeman field, chemical potential, and temperature, with a special emphasis on the roles played by the density…
We investigate the quantum phases of hard-core bosonic atoms in an extended Hubbard model where particles interact via soft-shoulder potentials in one dimension. Using a combination of field-theoretical methods and strong-coupling perturbation theory, we demonstrate that the low-energy phase can be a conformal cluster Luttinger liquid (CLL) phase with central charge $c=1$, where the microscopic degrees of freedom correspond to mesoscopic ensembles of particles. Using numerical density-matrix-renormalization-group methods, we demonstrate that the CLL phase, first predicted in [Phys. Rev. Lett. …
Ultracold atoms in optical lattice provides a platform to realize the superfluid (SF) state, a quantum order with paired charge-neutral fermions. In this paper, we studied SF state in the twodimensional attractive Hubbard model with pi-flux on each plaquette. The SF state in the pi-flux lattice model suffers very strong quantum fluctuations and the ground state becomes a possible quantum phase liquid state. In this phase, there exists the Cooper pairing together with a finite energy gap for the atoms, but no long range SF phase coherence exists at zero temperature. In addition, we discussed th…
Correlation functions and low-energy excitations are investigated in the asymmetric two-leg ladder consisting of a Hubbard chain and a noninteracting tight-binding (Fermi) chain using the density matrix renormalization group method. The behavior of charge, spin and pairing correlations is discussed for the four phases found at half filling, namely, Luttinger liquid, Kondo-Mott insulator, spin-gapped Mott insulator and correlated band insulator. Quasi-long-range antiferromagnetic spin correlations are found in the Hubbard leg in the Luttinger liquid phase only. Pair-density-wave correlations ar…
We explore the effects of geometric frustration within a one-dimensional Bose-Hubbard model using a chain of rhombi subject to a magnetic flux. The competition of tunnelling, self-interaction and magnetic flux gives rise to the emergence of a pair-superfluid (pair-Luttinger liquid) phase besides the more conventional Mott-insulator and superfluid (Luttinger liquid) phases. We compute the complete phase diagram of the model by identifying characteristic properties of the pair-Luttinger liquid phase such as pair correlation functions and structure factors and find that the pair-Luttinger liquid …
Bethe ansatz and bosonization procedures are used to describe the thermodynamics of the strong-coupled Hubbard chain in the \textit{spin-incoherent} Luttinger liquid (LL) regime: $J(\equiv 4t^2/U)\ll k_B T\ll E_F$, where $t$ is the hopping amplitude, $U(\gg t)$ is the repulsive on-site Coulomb interaction, and $k_B T (E_F\sim t)$ is the thermal (Fermi) energy. We introduce a fractional Landau LL approach, whose $U=\infty$ fixed point is exactly mapped onto an ideal gas with two species obeying the Haldane-Wu \textit{exclusion} fractional statistics. This phenomenological approach sheds light o…
One of the fundamental questions about the high temperature cuprate superconductors is the size of the Fermi surface (FS) underlying the superconducting state. By analyzing the single particle spectral function for the Fermi Hubbard model as a function of repulsion $U$ and chemical potential $μ$, we find that the Fermi surface in the normal state reconstructs from a large Fermi surface matching the Luttinger volume as expected in a Fermi liquid, to a Fermi surface that encloses fewer electrons that we dub the "Luttinger Breaking" (LB) phase, as the Mott insulator is approached. This transition…
In nonperturbative regimes, the superfluid instability in the two-dimensional Hubbard model can be described by an emergent BCS theory with small effective pairing constants. We compute the effective couplings using a controlled bold-line diagrammatic Monte Carlo approach, which stochastically sums all skeleton Feynman diagrams dressed in the one- and two-particle channels to high expansion orders, and map out the resulting superfluid ground-state phase diagram in a range of next-nearest-neighbor hopping $0 \leq t^{\prime} \leq 0.3t$, interaction strength $0 \leq U \leq 3t$, and lattice fillin…
By shifting the reference system for the local-density approximation (LDA) from the electron gas to other model systems one obtains a new class of density functionals, which by design account for the correlations present in the chosen reference system. This strategy is illustrated by constructing an explicit LDA for the one-dimensional Hubbard model. While the traditional {\it ab initio} LDA is based on a Fermi liquid (the electron gas), this one is based on a Luttinger liquid. First applications to inhomogeneous Hubbard models, including one containing a localized impurity, are reported.
We study the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (LP's) with increasing attraction, in the presence of the Zeeman magnetic field ($h$) for $d=2$, within the spin-polarized attractive Hubbard model. The broken symmetry Hartree approximation {as well as the} strong coupling expansion are used. We also apply the Kosterlitz-Thouless (KT) scenario to determine the phase coherence temperatures. For spin independent hopping integrals ($t^{\uparrow}=t^{\downarrow}$), we find no stable homogeneous polarized superfluid (SC$_M$) stat…
We calculate the correlation functions and the DC conductivity of Luttinger liquid superlattices, modeled by a repeated pattern of interacting and free Luttinger liquids. In a specific realization, where the interacting subsystem is a Hubbard chain, the system exhibits a rich phase diagram with four different phases: two metals and two compressible insulators. In general, we find that the effective low energy description amalgamates features of both types of liquids in proportion to their spatial extent, suggesting the interesting possibility of `engineered' Luttinger liquids.
We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on--site interaction U and a nearest--neighbor interaction V. We focus on the ground state phases of the model in the V >> U region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value V=V_PS. Using quantum Monte Carlo methods on lattices much larger than in previous Lanczos diagonalization studies, we determine the boundary of phase separation, the Luttinger Liquid correlat…
We investigate Luttinger Liquid superlattices, a periodic structure composed of two kinds of one-dimensional systems of interacting electrons. We calculate several properties of the low-energy sector: the effective charge and spin velocities, the compressibility, various correlation functions, the Landauer conductance and the Drude weight. The low-energy properties are subsumed into effective parameters, much like homogeneous one-dimensional systems. A generic result is the weighted average nature of these parameters, in proportion to the spatial extent of the underlying subunits, pointing to …
On the basis of an analysis of the numerical results corresponding to the half-filled 1D t-t'-V model on some finite lattices, Kokalj and Prelovsek (KP) have in a recent paper [Phys. Rev. B 78, 153103 (2008), arXiv:arXiv:0803.4468] concluded that the Luttinger theorem (LT) does not apply for the Mott-Hubbard (MH) insulating phase of this model (i.e. for V >> t) in the thermodynamic limit; KP even suggested, incorrectly, that failure of the LT were apparent for a half-filled finite system consisting of N=26 lattice sites. By employing a simple model for the self-energy Sigma of a MH state, we s…
The Tomonaga--Luttinger parameter $K_ρ$ determines the critical behavior in quasi one-dimensional correlated electron systems, e.g., the exponent $α$ for the density of states near the Fermi energy. We use the numerical density-matrix renormalization group method to calculate $K_ρ$ from the slope of the density-density correlation function in momentum space at zero wave vector. We check the accuracy of our new approach against exact results for the Hubbard and XXZ Heisenberg models. We determine $K_ρ$ in the phase diagram of the extended Hubbard model at quarter filling, $n_{\rm c}=1/2$, and c…
We investigate a system of one dimensional Hubbard chains of interacting fermions coupled by inter-chain hopping. Using a generalization of the Dynamical Mean Field Theory we study the deconfinement transition from a Mott insulator to a metal and the crossover between Luttinger and Fermi liquid phases. One-particle properties, local spin response and inter-chain optical conductivity are calculated. Possible applications to organic conductors are discussed.
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 the superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model through quantum Monte Carlo simulations. The Bose-Hubbard model is studied in the presence of site disorder and the quantum critical point between the Bose-glass and superfluid is determined in both the grand canonical ($μ/U=0.375$ close to $ρ=1$) and canonical ensemble ($ρ=1$ and 0.5). Particular attention is paid to disorder averaging and it is shown that an extremely large number of disorder realizations are needed in order to obtain reliable results. Typically we average over more than $…
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 study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid--alternating-Mott insulator phase transiti…
We predict that a new superfluid phase, the incompressible excitonic superfluid (IESF), in the phase diagram of ultracold Bose atoms in $d>1$ dimensional optical lattices, which is caused by the spontaneous breaking of the symmetry of translation of the lattice. Within mean field theory, the critical temperature of the phase transition from this IESF to the normal fluid (NF) is calculated and the triple-critical point of the three phases is determined. We also investigate both configuration and gauge field fluctuations and show the IESF state is stable against these fluctuations. We expect thi…
