R. T. Scalettar

Mott Domains of Bosons Confined on Optical Lattices

In the absence of a confining potential, the boson-Hubbard model exhibits a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong coupling. We use quantum Monte Carlo simulations to study the ground state of the one-dimensional bosonic Hubbard model in a trap. Some, but not all, aspects of the Mott insulating phase persist. Mott behavior occurs for a continuous range of incommensurate fillings, very different from the unconfined case, and the establishment of the Mott phase does not proceed via a traditional quantum phase transition. These results have important implications for interpreting experiments on ultracold atoms on optical lattices.

Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms

Ultracold atoms in optical lattices have great potential to contribute to a better understanding of some of the most important issues in many-body physics, such as high-temperature superconductivity. The Hubbard model—a simplified representation of fermions moving on a periodic lattice—is thought to describe the essential details of copper oxide superconductivity. This model describes many of the features shared by the copper oxides, including an interaction-driven Mott insulating state and an antiferromagnetic (AFM) state. Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realize the Hubbard model with readily tunable parameters, and thus provide a platform for the systematic exploration of its phase diagram. Realization of strongly correlated phases, however, has been hindered by the need to cool the atoms to temperatures as low as the magnetic exchange energy, and also by the lack of reliable thermometry. Here we demonstrate spin-sensitive Bragg scattering of light to measure AFM spin correlations in a realization of the three-dimensional Hubbard model at temperatures down to 1.4 times that of the AFM phase transition. This temperature regime is beyond the range of validity of a simple high-temperature series expansion, which brings our experiment close to the limit of the capabilities of current numerical techniques, particularly at metallic densities. We reach these low temperatures using a compensated optical lattice technique, in which the confinement of each lattice beam is compensated by a blue-detuned laser beam. The temperature of the atoms in the lattice is deduced by comparing the light scattering to determinant quantum Monte Carlo simulations and numerical linked-cluster expansion calculations. Further refinement of the compensated lattice may produce even lower temperatures which, along with light scattering thermometry, would open avenues for producing and characterizing other novel quantum states of matter, such as the pseudogap regime and correlated metallic states of the two-dimensional Hubbard model.

Cerium Volume Collapse: Results from the Merger of Dynamical Mean-Field Theory and Local Density Approximation

The merger of density-functional theory in the local density approximation (LDA) and many-body dynamical mean field theory (DMFT) allows for an ab initio calculation of Ce including the inherent 4f electronic correlations. We solve the DMFT equations by the quantum Monte Carlo (QMC) technique and calculate the Ce energy, spectrum, and double occupancy as a function of volume. At low temperatures, the correlation energy exhibits an anomalous region of negative curvature which drives the system towards a thermodynamic instability, i.e., the

Local quantum criticality in confined fermions on optical lattices.

\gamma

Collapse of magnetic moment drives the Mott transition in MnO

-to-

CDW AND SDW MEDIATED PAIRING INTERACTIONS

\alpha

Quantum phase transitions in the two-dimensional hardcore boson model

volume collapse, consistent with experiment. The connection of the energetic with the spectral evolution shows that the physical origin of the energy anomaly and, thus, the volume collapse is the appearance of a quasiparticle resonance in the 4f-spectrum which is accompanied by a rapid growth in the double occupancy.

Superconductivity and Lattice Instability in Compressed Lithium from Fermi Surface Hot Spots

Using quantum Monte Carlo simulations, we show that the one-dimensional fermionic Hubbard model in a harmonic potential displays quantum critical behavior at the boundaries of a Mott-insulating region. A local compressibility defined to characterize the Mott-insulating phase has a nontrivial critical exponent. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We determine a generic phase diagram, which allows the prediction of the phases to be observed in experiments with ultracold fermionic atoms trapped on optical lattices.

Thermodynamic and spectral properties of compressed Ce calculated using a combined local-density approximation and dynamical mean-field theory

Summary and Outlook These results demonstrate that the underlying LDA band structure, buttressed by on-site inter-actions (U, J) treated within the dynamical DMFT ansatz, provide a realistic description of theMott transition in MnO without input from experiment. This study finally allows a determinationof the mechanism of the transition, which could not be uncovered by experiment alone: the mag-netic moment collapse, volume collapse, and metal-insulator transitions occur simultaneously, butit is the increasing crystal field splitting (encroachment of the O 2− ion on the internal structure ofthe Mn ion) and not the increasing bandwidth that tips the balance.The current results illustrate success of the LDA+DMFT approach in describing a pressure-driven Mott transition in a strongly correlated insulator, joining the growing number of successesof this approach in other strongly correlated real materials. The Kondo volume collapse tran-sition in Ce 15,28 and other elemental lanthanides, 29 and the realistic modeling of parts of thecomplex phase diagram

REVISITING THE THEORY OF FINITE SIZE SCALING IN DISORDERED SYSTEMS : NU CAN BE LESS THAN 2/D

Pairing near CDW and SDW metal-semiconductor transitions is analyzed for a 2-D lattice within an RPA approximation. We find that s-wave pairing can occur near the CDW transition provided the on-site U is not too large, while d-wave pairing occurs near an SDW transition.