Spin singlet mott states and evidence for spin singlet quantum condensates of spin-one bosons in lattices

We have investigated spin singlet Mott states of spin-one bosons with antiferromagnetic interactions. These spin singlet states do not break rotational symmetry and exhibit remarkably different macroscopic properties compared with nematic Mott states of spin-one bosons. We demonstrate that the dynamics of spin singlet Mott states is fully characterized by even- or odd-class quantum dimer models. The difference between spin singlet Mott states for even and odd numbers of atoms per site can be attributed to a selection rule in the low energy sectors of on-site Hilbert spaces; alternatively, it can also be attributed to an effect of Berry’s phases on bosonic Mott states. We also discuss evidence for spin singlet quantum condensate of spin-one atoms. Our main finding is that in a projected spin singlet Hilbert space, the low energy physics of spin-one bosons is equivalent to that of a Bose-Hubbard model for spinless bosons interacting via Ising gauge fields. The other major finding is spin-charge separation in some one-dimensional Mott states. We propose charge-e spin singlet superfluid for an odd number of atoms per lattice site and charge-2e spin singlet superfluid for an even number of atoms per lattice site in one-dimensional lattices. All discussions in this article are limited to integer numbers of bosons per site.     

Dual vortex theory of doped Mott insulators

We present a general framework for describing the quantum phases obtained by doping paramagnetic Mott insulators on the square lattice. The undoped insulators are efficiently characterized by the projective transformations of various fields under the square lattice space group (the PSG). We show that the PSG also imposes powerful constraints on the doped system, and on the effective action for the vortex and Bogoliubov quasiparticle excitations of superconducting states. This action can also be extended across transitions to supersolid or insulating states at non-zero doping. For the case of a valence bond solid (VBS) insulator, we show that the doped system has the same PSG as that of elementary bosons with density equal to the density of electron Cooper pairs. We also discuss aspects of the action for a d-wave superconductor obtained by doping a “staggered-flux” spin liquid state.     

Breakdown of Luttinger's theorem in two-orbital Mott insulators

An analysis of Luttinger's theorem shows that – contrary to recent claims – it is not valid for a generic Mott insulator. For a two-orbital Hubbard model with two electrons per site the crossover from a non-magnetic correlated insulating phase (Mott or Kondo insulator) to a band insulator is investigated. Mott insulating phases are characterized by poles of the self-energy and corresponding zeros in the Greens functions defining a “Luttinger surface” which is absent for band insulators. Nevertheless, the ground states of such insulators with two electrons per unit cell are adiabatically connected.     

Topological Mott insulators

We consider extended Hubbard models with repulsive interactions on a honeycomb lattice, and the transitions from the semimetal to Mott insulating phases at half-filling. Because of the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spin fermion models, respectively. The mean-field phase diagram is presented and the fluctuations are treated within the random phase approximation. Renormalization group analysis shows that these states can be favored over the topologically trivial Mott insulating states.     

Imaging nanoscale electronic inhomogeneity in the lightly doped Mott insulator Ca(2-x)NaxCuO2Cl2

The spatial variation of electronic states was imaged in the lightly doped Mott insulator Ca(2-x)NaxCuO2Cl2 using scanning tunneling microscopy or spectroscopy. We observed nanoscale domains with a high local density of states within an insulating background. The observed domains have a characteristic length scale of 2 nm (approximately 4-5a, a: lattice constant) with preferred orientations along the tetragonal [100] direction. We argue that such spatially inhomogeneous electronic states are inherent to slightly doped Mott insulators and play an important role for the insulator to metal transition.     

Classifying novel phases of spinor atoms

We consider many-body states of bosonic spinor atoms which, at the mean-field level, can be characterized by a single-particle wave function for the Bose-Einstein condensation and Mott insulating states. We describe and apply a classification scheme that makes explicit the spin symmetries of such states and enables one to naturally analyze their collective modes and topological excitations. Quite generally, the method allows classification of a spin F system as a polyhedron with 2F vertices. We apply the method to the many-body states of bosons with spins two and three. For spin-two atoms we find the ferromagnetic state, a continuum of nematic states, and a state having the symmetry of the point group of the regular tetrahedron. For spin-three atoms we obtain similar ferromagnetic and nematic phases as well as states having symmetries of various types of polyhedra with six vertices.     

Noise correlation spectroscopy of the broken order of a Mott insulating phase

We use a two-color lattice to break the homogeneous site occupation of an atomic Mott insulator of bosonic 87Rb. We detect the disruption of the ordered Mott domains via noise correlation analysis of the atomic density distribution after time of flight. The appearance of additional correlation peaks evidences the redistribution of the atoms into a strongly inhomogeneous insulating state, in quantitative agreement with the predictions.     

Quantum phase transition of cold atoms trapped in optical lattices

We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.     

Pseudogap in doped Mott insulators is the near-neighbor analogue of the Mott gap

We show that the strong-coupling physics inherent to the insulating Mott state in 2D leads to a jump in the chemical potential upon doping and the emergence of a pseudogap in the single-particle spectrum below a characteristic temperature. The pseudogap arises because any singly occupied site not immediately neighboring a hole experiences a maximum energy barrier for transport equal to t(2)/U, t the nearest-neighbor hopping integral and U the on-site repulsion. The resultant pseudogap cannot vanish before each lattice site, on average, has at least one hole as a near neighbor. The ubiquity of this effect in all doped Mott insulators suggests that the pseudogap in the cuprates has a simple origin.     

Coherent transport of neutral atoms in spin-dependent optical lattice potentials

We demonstrate the controlled coherent transport and splitting of atomic wave packets in spin-dependent optical lattice potentials. Such experiments open intriguing possibilities for quantum state engineering of many body states. After first preparing localized atomic wave functions in an optical lattice through a Mott insulating phase, we place each atom in a superposition of two internal spin states. Then state selective optical potentials are used to split the wave function of a single atom and transport the corresponding wave packets in two opposite directions. Coherence between the wave packets of an atom delocalized over up to seven lattice sites is demonstrated.     

Creation of a molecular condensate by dynamically melting a Mott insulator

We propose the creation of a molecular Bose-Einstein condensate by loading an atomic condensate into an optical lattice and driving it into a Mott insulator with exactly two atoms per site. Molecules in a Mott insulator state are then created under well defined conditions by photoassociation with essentially unit efficiency. Finally, the Mott insulator is melted and a superfluid state of the molecules is created. We study the dynamics of this process and photoassociation of tightly trapped atoms.     

Detecting correlation functions of ultracold atoms through fourier sampling of time-of-flight images

We propose a detection method for ultracold atoms which allows reconstruction of the full one-particle and two-particle correlation functions from the measurements. The method is based on Fourier sampling of the time-of-flight images through two consecutive impulsive Raman pulses. For applications of this method, we discuss a few examples, including detection of phase separation between superfluid and Mott insulators, various types of spin or superfluid orders, entanglement, exotic or fluctuating orders.     

Sizable band gap in organometallic topological insulator

Based on first principle calculation when Ceperley–Alder and Perdew–Burke–Ernzerh type exchange-correlation energy functional were adopted to LSDA and GGA calculation, electronic properties of organometallic honeycomb lattice as a two-dimensional topological insulator was calculated. In the presence of spin–orbit interaction bulk band gap of organometallic lattice with heavy metals such as Au, Hg, Pt and Tl atoms were investigated. Our results show that the organometallic topological insulator which is made of Mercury atom shows the wide bulk band gap of about ∼120 meV. Moreover, by fitting the conduction and valence bands to the band-structure which are produced by Density Functional Theory, spin–orbit interaction parameters were extracted. Based on calculated parameters, gapless edge states within bulk insulating gap are indeed found for finite width strip of two-dimensional organometallic topological insulators.     

Symmetry of the superconducting order parameter in frustrated systems determined by the spatial anisotropy of spin correlations

We study the resonating valence bond theory of the Hubbard-Heisenberg model on the half-filled anisotropic triangular lattice. Varying the frustration changes the wave vector of maximum spin correlation in the Mott insulating phase. This, in turn, changes the symmetry of the superconducting state that occurs at the boundary of the Mott insulating phase. We propose that this physics is realized in several families of quasi-two-dimensional organic superconductors.     

Linear response calculations of lattice dynamics in strongly correlated systems

We introduce a new linear response method to study the lattice dynamics of materials with strong correlations. It is based on a combination of dynamical mean field theory of strongly correlated electrons and the local density functional theory of electronic structure. We apply the method to study the phonon dispersions of Mott insulators NiO and MnO in their paramagnetic insulating state not accessible by local density functionals. Our results are in good agreement with experiment.     

Hidden order in 1D bose insulators

We investigate the phase diagram of spinless bosons with long range (variant 1/r(3)) repulsive interactions, relevant to ultracold polarized atoms or molecules, using density matrix renormalization group. Between the two conventional insulating phases, the Mott and density wave phases, we find a new phase possessing hidden order revealed by nonlocal string correlations analogous to those characterizing the Haldane gapped phase of integer spin chains. We develop a mean field theory that describes the low-energy excitations in all three insulating phases. This is used to calculate the absorption spectrum due to oscillatory lattice modulation. We predict a sharp resonance in the spectrum due to a collective excitation of the new phase that would provide clear evidence for the existence of this phase.     

Ultrafast optical pumping of spin and orbital polarizations in the antiferromagnetic Mott insulators R(2)CuO(4)

We demonstrate that optical pumping by circularly polarized light at the charge-transfer transition can induce spin and orbital polarizations in the strongly correlated Mott insulators R(2)CuO(4) (R=Pr, Nd, Sm) providing a means of ultrafast nonlinear manipulation of spin states on time scales of less than 150 fs. We propose a model which includes both orbital- and spin-related processes possessing different spectral and temporal properties. This allows us to model the optical response of antiferromagnetic Mott insulators to circularly polarized light and estimate the spin relaxation time as tau(s) approximately 30-50 fs.     

Magnetization plateaus for spin-one bosons in optical lattices: Stern-Gerlach experiments with strongly correlated atoms

We consider insulating states of spin-one bosons in optical lattices in the presence of a weak magnetic field. For the states with more than one atom per lattice site we find a series of quantum phase transitions between states with fixed magnetization and a canted nematic phase. In the presence of a global confining potential, this unusual phase diagram leads to several novel phenomena, including the formation of magnetization plateaus. We discuss how these effects can be observed using spatially resolved spin polarization measurements.     

Electronic structure of Mott insulators

Mott insulators are identified here with ordinary magnetic insulators. The insulating gap, local moment, and effective spin hamiltonian aspects are qualitatively explained by means of a novel set of solutions of the Hartree-Fock equations. The apparent conflict between Bloch's theorem and localized-electron phenomenology is thereby resolved in an elementary manner. This Hartree-Fock approach also sheds considerable light on the physical mechanisms responsible for the associated metal-insulator (Mott) and other related phase transitions, as observed in V₂O₃ and several other materials. With some generalizations and refinements, this theoretical picture is shown to also account semiquantitatively for a number of detailed properties of NiO and CoO, two of the most extensively studied Mott insulator materials. A wide variety of experimental data for NiO is surveyed in order to determine reasonable values for its effective Hubbard hamiltonian parameters, suitably generalized for the 3d electrons. The problems of formally deriving effective spin hamiltonians for macroscopic magnetic insulator systems are also carefully examined. The old non-orthogonality catastrophe is fully resolved by means of a degenerate (open-shell) analogue of the linked cluster perturbation expansion of Brueckner and Goldstone. Although many quantitative issues remain, these results indicate that there is now a reasonably adequate conceptual understanding of the Mott insulating state.     

Quasiparticle bands in cuprates by quantum-chemical methods: towards an ab initio description of strong electron correlations

Realistic electronic-structure calculations for correlated Mott insulators are notoriously difficult. Here we present an ab initio multiconfiguration scheme that adequately describes strong correlation effects involving Cu 3d and O 2p electrons in layered cuprates. In particular, the O 2p states giving rise to the Zhang-Rice band are explicitly considered. Renormalization effects due to nonlocal spin interactions are also treated consistently. We show that the dispersion of the lowest band observed in photoemission is reproduced with quantitative accuracy. Additionally, the evolution of the Fermi surface with doping follows directly from our ab initio data. Our results thus open a new avenue for the first-principles investigation of the electronic structure of correlated Mott insulators.