Orbital selective crossover and Mott transitions in an asymmetric Hubbard model of cold atoms in optical lattices

We study the asymmetric Hubbard model at half-filling as a generic model to describe the physics of two species of repulsively interacting fermionic cold atoms in optical lattices. We use Dynamical Mean Field Theory to obtain the paramagnetic phase diagram of the model as function of temperature, interaction strength and hopping asymmetry. A Mott transition with a region of two coexistent solutions is found for all nonzero values of the hopping asymmetry. At low temperatures the metallic phase is a heavy Fermi-liquid, qualitatively analogous to the Fermi liquid state of the symmetric Hubbard model. Above a coherence temperature, an orbital-selective crossover takes place, wherein one fermionic species effectively localizes, and the resulting bad metallic state resembles the non-Fermi liquid state of the Falicov-Kimball model. We compute observables relevant to cold atom systems such as the double occupation, the specific heat and entropy and characterize their behavior in the different phases

Weak coupling study of decoherence of a qubit in disordered magnetic environments

We study the decoherence of a qubit weakly coupled to frustrated spin baths. We focus on spin-baths described by the classical Ising spin glass and the quantum random transverse Ising model which are known to have complex thermodynamic phase diagrams as a function of an external magnetic field and temperature. Using a combination of numerical and analytical methods, we show that for baths initally in thermal equilibrium, the resulting decoherence is highly sensitive to the nature of the coupling to the environment and is qualitatively different in different parts of the phase diagram. We find an unexpected strong non-Markovian decay of the coherence when the random transverse Ising model bath is prepared in an initial state characterized by a finite temperature paramagnet. This is contrary to the usual case of exponential decay (Markovian) expected for spin baths in finite temperature paramagnetic phases, thereby illustrating the importance of the underlying non-trivial dynamics of interacting quantum spinbaths.Comment: 12 pages, 18 figure

Phase diagram of the asymmetric Hubbard model and an entropic chromatographic method for cooling cold fermions in optical lattices

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 density distribution is a good probe of this orbital selective crossover from a Fermi liquid to a non-Fermi liquid state. Below an ordering temperature $T_o$, which is a function of both the interaction and hopping asymmetry, the system exhibits staggered long range orbital order. Apart from the special case of the symmetric limit, i.e., Hubbard model, where there is no hopping asymmetry, this orbital order is accompanied by a true charge density wave order for all values of the hopping asymmetry. We calculate the order parameters and various physical quantities including the thermodynamics in both the ordered and disordered phases. We find that the formation of the charge density wave is signaled by an abrupt increase in the sublattice double occupancies. Finally, we propose a new method, entropic chromatography, for cooling fermionic atoms in optical lattices, by exploiting the properties of the AHM. To establish this cooling strategy on a firmer basis, we also discuss the variations in temperature induced by the adiabatic tuning of interactions and hopping parameters.Comment: 16 pages, 19 fig

Landau Theory of the Finite Temperature Mott Transition

In the context of the dynamical mean-field theory of the Hubbard model, we identify microscopically an order parameter for the finite temperature Mott endpoint. We derive a Landau functional of the order parameter. We then use the order parameter theory to elucidate the singular behavior of various physical quantities which are experimentally accessible.Comment: 4 pages, 2 figure

Non-equilibrium electronic transport in a one-dimensional Mott insulator

We calculate the non-equilibrium electronic transport properties of a one-dimensional interacting chain at half filling, coupled to non-interacting leads. The interacting chain is initially in a Mott insulator state that is driven out of equilibrium by applying a strong bias voltage between the leads. For bias voltages above a certain threshold we observe the breakdown of the Mott insulator state and the establishment of a steady-state electronic current through the system. Based on extensive time-dependent density matrix renormalization group simulations, we show that this steady-state current always has the same functional dependence on voltage, independent of the microscopic details of the model and relate the value of the threshold to the Lieb-Wu gap. We frame our results in terms of the Landau-Zener dielectric breakdown picture. Finally, we also discuss the real-time evolution of the current, and characterize the current-carrying state resulting from the breakdown of the Mott insulator by computing the double occupancy, the spin structure factor, and the entanglement entropy.Comment: 12 pages RevTex4, 12 eps figures, as published, minor revision

First-Order Insulator-to-Metal Mott Transition in the Paramagnetic 3D System GaTa4Se8

The nature of the Mott transition in the absence of any symmetry braking remains a matter of debate. We study the correlation-driven insulator-to-metal transition in the prototypical 3D Mott system GaTa4Se8, as a function of temperature and applied pressure. We report novel experiments on single crystals, which demonstrate that the transition is of first order and follows from the coexistence of two states, one insulating and one metallic, that we toggle with a small bias current. We provide support for our findings by contrasting the experimental data with calculations that combine local density approximation with dynamical mean-field theory, which are in very good agreement.Comment: 5 pages and 4 figures. Supplemental material: 2 pages, 2 figure

Equation of motion approach to the Hubbard model in infinite dimensions

We consider the Hubbard model on the infinite-dimensional Bethe lattice and construct a systematic series of self-consistent approximations to the one-particle Green's function, $G^{(n)}(\omega),\ n=2,3,\dots\$ . The first $n-1$ equations of motion are exactly fullfilled by $G^{(n)}(\omega)$ and the $n$'th equation of motion is decoupled following a simple set of decoupling rules. $G^{(2)}(\omega)$ corresponds to the Hubbard-III approximation. We present analytic and numerical results for the Mott-Hubbard transition at half filling for $n=2,3,4$.Comment: 10pager, REVTEX, 8-figures not available in postscript, manuscript may be understood without figure

Transfer of Spectral Weight in Spectroscopies of Correlated Electron Systems

We study the transfer of spectral weight in the photoemission and optical spectra of strongly correlated electron systems. Within the LISA, that becomes exact in the limit of large lattice coordination, we consider and compare two models of correlated electrons, the Hubbard model and the periodic Anderson model. The results are discussed in regard of recent experiments. In the Hubbard model, we predict an anomalous enhancement optical spectral weight as a function of temperature in the correlated metallic state which is in qualitative agreement with optical measurements in $V_2O_3$. We argue that anomalies observed in the spectroscopy of the metal are connected to the proximity to a crossover region in the phase diagram of the model. In the insulating phase, we obtain an excellent agreement with the experimental data and present a detailed discussion on the role of magnetic frustration by studying the $k-$resolved single particle spectra. The results for the periodic Anderson model are discussed in connection to recent experimental data of the Kondo insulators $Ce_3Bi_4Pt_3$ and $FeSi$. The model can successfully explain the different energy scales that are associated to the thermal filling of the optical gap, which we also relate to corresponding changes in the density of states. The temperature dependence of the optical sum rule is obtained and its relevance for the interpretation of the experimental data discussed. Finally, we argue that the large scattering rate measured in Kondo insulators cannot be described by the periodic Anderson model.Comment: 19 pages + 29 figures. Submitted to PR

Mott transition at large orbital degeneracy: dynamical mean-field theory

We study analytically the Mott transition of the N-orbital Hubbard model using dynamical mean-field theory and a low-energy projection onto an effective Kondo model. It is demonstrated that the critical interaction at which the insulator appears (Uc1) and the one at which the metal becomes unstable (Uc2) have different dependence on the number of orbitals as the latter becomes large: Uc1 ~ \sqrt{N} while Uc2 ~ N. An exact analytical determination of the critical coupling Uc2/N is obtained in the large-N limit. The metallic solution close to this critical coupling has many similarities at low-energy with the results of slave boson approximations, to which a comparison is made. We also discuss how the critical temperature associated with the Mott critical endpoint depends on the number of orbitals.Comment: 13 pages. Minor changes in V