Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session W12: Metal Insulator Transition II: Theory |
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Sponsoring Units: DCMP Chair: Jim Freericks, Georgetown University Room: Morial Convention Center 203 |
Thursday, March 13, 2008 2:30PM - 2:42PM |
W12.00001: Effect of frustration on charge dynamics for a doped two-dimensional triangular Hubbard lattice Takami Tohyama We examine the optical conductivity $\sigma(\omega)$ and the chemical potential $\mu$, together with the spin correlation, in the strong-coupling limit of a hole-doped two-dimensional triangular Hubbard model near half filling by using an exact diagonalization technique [1]. In contrast to the case of a square lattice without frustration, the doping dependences of $\mu$ and the Drude weight indicate that the charge degree of freedom is weakly coupled to the spin degree of freedom. However, we find that $\sigma(\omega)$ shows strong incoherent excitations extended to a higher energy region. This implies that geometrical frustration in strongly correlated electron systems influences incoherent charge dynamics. Momentum- dependent charge dynamics is also compared with that of the square lattice. [Preview Abstract] |
Thursday, March 13, 2008 2:42PM - 2:54PM |
W12.00002: Exact diagonalization analysis of the Anderson-Hubbard model and comparison to real-space self-consistent Hartree-Fock solutions Xi Chen, Pakwo Leung, Robert Gooding We have obtained the exact ground state wave functions of the Anderson-Hubbard model for different electron fillings on a 4x4 lattice with periodic boundary conditions. When compared to the uncorrelated ground states (Hubbard interaction set to zero) we have found evidence of very effective screening, producing smaller charge inhomogeneities due to the Hubbard interaction, particularly at 1/2 filling, and have successfully modelled these local charge densities with non-interacting electrons that experience a static screening of the impurity potentials. Further, we have compared such wave functions to self-consistent real-space unrestricted Hartree-Fock solutions and have found that these approximate ground state wave functions are very successful at reproducing the local charge densities, and may indicate the role of dipolar backflow in producing a novel metallic state in two dimensions. [Preview Abstract] |
Thursday, March 13, 2008 2:54PM - 3:06PM |
W12.00003: Electronic Griffiths phase near a disordered Mott transition in $D=2$ Eric Andrade, Eduardo Miranda, Vlad Dobrosavljevic We investigate the effects of weak and moderate disorder on the $T=0$ Mott Metal-Insulator Transition (MIT) in two dimensions, by solving the disordered Hubbard Model within the so-called Statistical Dynamical Mean Field Theory (statDMFT) {[}1]. In the weak disorder regime, we recover the results of the standard DMFT limit {[}2], including strong disorder screened close to the MIT. For moderate disorder, the screening of the disorder remains strong, but is reduced by fluctuation effects absent in high dimensions. For disorder strength $W$ smaller then the on-site interaction $U$, the transition retains the Mott character, where the local quasiparticles weights $Z_{i}$ vanish on all sites at the transition, indicating the transmutation of all electron into local magnetic moments. In contrast to the behavior in high dimensions {[}2], the corresponding distribution function $P\left(Z\right)$ is found to assume a singular form as the transition is approached, indicating the emergence of an electronic Griffiths phase {[}3] preceding the MIT. \\ {[}1] V. Dobrosavljevic and G. Kotliar, Phys. Rev. Lett. 78, 3943 (1997). \\ {[}2] D. Tanaskovic et al, Phys. Rev. Lett. 91, 066603 (2003). \\ {[}3] E. Miranda and V. Dobrosavljevic, Phys. Rev. Lett. 86, 264 (2001). [Preview Abstract] |
Thursday, March 13, 2008 3:06PM - 3:18PM |
W12.00004: An Exactly Solvable Model with a Tunable Mott Gap without Broken Symmetry Daniel Hansen, B. Sriram Shastry The 1d Hubbard model at half filling provides the only known example of a Mott Hubbard insulating state, with a Mott charge gap without any concomittant broken symmetry. Such a state has inspired much current work in correlated matter in low dimensions. We present a model, where the Mott gap can be manipulated and infact made to vanish with some parameter. Using the higher conserved currents found by Shastry in 1986 for the 1-d Hubbard model, we construct a new model {\em which does show a tunable Mott gap}. The model is given by the hamiltonian $$H = H_{Hubbard}(U) + \lambda \; I_3(U),$$ where $H_{Hubbard}$ is the Hubbard hamiltonian and $I_3$ is its third conserved current. The new model has exactly the same space time symmetries as the Hubbard model, but possesses {\em two parameters}, $U ,\; \lambda$. The phase diagram in $\lambda-U$ is explored using numerical methods and the Bethe Ansatz. It displays several interesting features including a ``superconducting'' type state. A significant role is played by a band transition at $U=0$ (similar to the Lifshitz transition), wherein the two fermi points of the Hubbard model break up into 6 Fermi points. We also find a variety of second order transitions. [Preview Abstract] |
Thursday, March 13, 2008 3:18PM - 3:30PM |
W12.00005: Insulator-Insulator Transitions in an Ionic Hubbard Model Ara Go, Gun Sang Jeon We study the ionic Hubbard model in one and two dimensions at zero temperature. As the Hubbard interaction is increased, the system is known to evolve from a band insulator to a Mott insulator. The former phase is induced by the alternating on-site potential energy while the strong local Hubbard interaction drives the system towards correlated Mott insulator. In order to examine the transition nature, we perform the cellular dynamical mean-field calculation with an exact diagonalization technique employed as an impurity solver. From the computed local density of states we estimates the spectral gap as the interaction strength is varied. We also calculate the momentum-dependent density of states which exhibits characteristic features for different phases. [Preview Abstract] |
Thursday, March 13, 2008 3:30PM - 3:42PM |
W12.00006: Metal-Insulator Transitions in the Periodic Anderson Model Giovanni Sordi, Adriano Amaricci, Marcelo Rozenberg We investigate the doping driven metal-insulator transition in the periodic Anderson model in the Mott-Hubbard regime, using dynamical mean-field theory. Upon electron doping of the Mott-insulator, a metal-insulator transition occurs, which shares the same qualitative features of the first order transition found in the single band Hubbard model. Surprisingly, upon hole doping, the metal-insulator transition is not first order. Thus our study demonstrate that the transition scenario of the single band Hubbard model is not generic for the periodic Anderson model, even in the Mott-Hubbard regime. {\sl Phys. Rev. Lett.} {\bf 99}, 196403 (2007) [Preview Abstract] |
Thursday, March 13, 2008 3:42PM - 3:54PM |
W12.00007: The Anderson-Mott transition for a correlated 2D system Maria Elisabetta Pezzoli, Federico Becca, Giuseppe Santoro, Michele Fabrizio The interplay of disorder and electron-electron interaction can lead a bidimensional system to different phase transitions. We show that the Gutzwiller wave function generalized for an inhomogeneous system and with a long-term Jastrow factor provides a proper variational description of the Mott insulating phase and of the compressible disordered phase. Moreover, we identify an order parameter for the disordered Mott transition both in the paramagnetic and in the magnetic case. [Preview Abstract] |
Thursday, March 13, 2008 3:54PM - 4:06PM |
W12.00008: The 2D Metal-Insulator Transition: A percolative Monte Carlo study Donald Priour Jr., Sankar Das Sarma We examine the metal-insulator transition (MIT) in two dimensional electronic systems (e.g. n doped GaAs heterostructures) in the presence of a long-range Coulombic random potential set up by a nearby layer of charged impurities. An iterative scheme taking into account nonlinear screening is used to obtain the inhomogeneous ``landscape'' of electron-rich and electron-depleted regions. The percolation (or not) of electron rich areas (in the regime of electronic densities $n$ where linear screening breaks down) is determined by a variant of the Hoshen Kopelman algorithm. Identifying the percolation transition as the metal-insulator transition, we calculate the critical electron density $n_{c}$ as a function of the concentration of charged impurities, the separation $d$ of the impurity layer from the electronic layer, and the thickness of the impurity rich region; the effect of correlated impurity positions is also examined. Using finite size scaling analysis, we calculate the critical exponent $\delta$ for the asymptotic scaling $\sigma \propto (n - n_{c})^{\delta}$ in the vicinity of the MIT. We acknowledge support from US-ONR and NRI-NSF. [Preview Abstract] |
Thursday, March 13, 2008 4:06PM - 4:18PM |
W12.00009: Quantum and thermal fluctuation effects on solid-light systems Martin Hohenadler, Markus Aichhorn, Charles Tahan, Peter Littlewood Several theoretical proposals of strongly correlated polariton systems which exhibit a quantum phase transition from a Mott insulator to a superfluid phase have recently been made. Here we study Mott phases of polaritons in a model of optical microcavities in a photonic crystal with nearest-neighbor photon hopping. The variational cluster approach takes into account quantum fluctuations exactly on the lengthscale of finite clusters, and yields phase diagrams and single-particle spectra at zero and finite temperature in one and two dimensions. The relation of the model to the well-known Bose-Hubbard model is explored, and implications of our findings concerning the stability of the Mott state at finite temperatures for technological applications are discussed. [Preview Abstract] |
Thursday, March 13, 2008 4:18PM - 4:30PM |
W12.00010: Effects of electron correlations on delocalization and percolation of electronic states Kendall Mallory A simulation of the effects of electron correlations on the formation of delocalized states and percolating clusters is presented. The model includes disorder in site locations and energy and uses a semi-classical approach to finding matrix elements and diagonalizing the Hamiltonian. We are also looking for scale invariant properties in the system. [Preview Abstract] |
Thursday, March 13, 2008 4:30PM - 4:42PM |
W12.00011: Dynamic mean-field theory of the ionic Hubbard model Ji-Woo Lee, Gun Sang Jeon We study the ionic Hubbard model in the infinite dimensions in the framework of dynamical mean-field theory. Exact diagonalization is used to obtain the impurity Green's function to satisfy the self-consistant equation. We obtain a phase diagram in the parameter space of local ionic potential strength, $\Delta$ and local repulsive energy, $U$ exhibiting three phases: Mott insulator, metal, band insulator. Analyzing the spectral density, we compare our results with those of iterative perturbation theory and quantum Monte Carlo study in two dimensions. [Preview Abstract] |
Thursday, March 13, 2008 4:42PM - 4:54PM |
W12.00012: Evolution of the Mott-Hubbard insulator transition in bulk nonequilibrium; dynamical mean field theory Ryan Heary, Jong Han The equilibrium dynamical mean-field theory (DMFT) is extended to the steady-state nonequilirium in which the Hubbard lattice is populated by left and right movers. The nonequilibrium boundary condition is imposed in the non-interacting limit by applying a chemical potential shift between the left and right movers of the homogeneous bulk system. The success of this theory lies in the fact that the local Green function can be calculated nonperturbatively using the imaginary-time formulation of the steady-state nonequilibrium [1]. We study the evolution of metallic quasi-particle excitations near the Mott-Hubbard insulator transition as a function of the chemical potential bias. The nonequilibrium DMFT algorithm will be presented along with the nonlinear nonequilibirum destruction of the Kondo resonance. \newline [1] J. E. Han, R. J. Heary, Imaginary-time formulation of steady-state nonequilibrium: application to strongly correlated transport, {\it accepted to Phys. Rev. Lett.} arXiv:0704.3198. [Preview Abstract] |
Thursday, March 13, 2008 4:54PM - 5:06PM |
W12.00013: Non-local Coulomb correlations in metals close to a charge order insulator transition Jaime Merino Recent extensions of dynamical mean-field theory (DMFT) to clusters either in its real space (CDMFT) or momentum space versions (DCA) have become important tools for the description of electronic properties of low dimensional strongly correlated systems. In contrast to single site DMFT, short range correlation effects on electronic properties of systems close to the Mott transition can be analyzed. We have investigated the charge ordering transition induced by the nearest-neighbor Coulomb repulsion V in the 1/4-filled extended Hubbard model using CDMFT. We find a transition to a strongly renormalized charge ordered Fermi liquid at V$_{\mathrm{CO}}$ and a metal-to- insulator transition at V$_{\mathrm{MI}}>$V$_{\mathrm{CO}}$. Short range antiferromagnetism occurs concomitantly with the CO transition. Approaching the charge ordered insulator, V$<$V$_ {\mathrm{MI}}$, the Fermi surface deforms and the scattering rate of electrons develops momentum dependence on the Fermi surface. [Preview Abstract] |
Thursday, March 13, 2008 5:06PM - 5:18PM |
W12.00014: Exact steady state non-equilibrium DOS of the Hubbard model Alexander Joura, Jim Freericks, Thomas Pruschke Using a non-equilibrium Kadanoff-Baym-Keldysh formalism, we derive exact equations relating the retarded Green's function to the retarded self-energy for lattice electrons in presence of a constant and uniform electric field $E$. Such an approach allows us to go beyond linear response theory and study the behavior of systems for arbitrarily large electric fields. We find that the conventional dynamical mean-field theory (DMFT) algorithm is the same as in equilibrium except for a significantly modified lattice Dyson equation which couples together frequencies separated by the Bloch frequency. We apply the method to the Hubbard model and solve the model within the DMFT framework. As an impurity solver, we employ the numerical renormalization group (NRG). We discuss how the density of states (DOS) evolves as the electric field strength $E$ and interaction strength $U$ change. In particular, when both $E\ll1$ and $U\ll1$ the DOS is a set of equally spaced peaks (the so called Wannier-Stark ladder). Increasing $U$ leads to a broadening of the peaks, which finally merge and then evolve into a DOS that is quite similar to the equilibrium DOS. Increasing $E$ while keeping $U\ll1$ splits the peaks, resulting in novel behavior for the DOS, which is reminiscent of a metal-insulator transition (but the system carries current). [Preview Abstract] |
Thursday, March 13, 2008 5:18PM - 5:30PM |
W12.00015: Mott transition and Universality at finite temperatures Stefanos Papanikolaou, Rafael M. Fernandes, Eduardo Fradkin, Philip W. Phillips, Joerg Schmalian, Rastko Sknepnek We consider the finite temperature Mott critical point which has been the subject of recent experimental investigation. We demonstrate that this critical point is in the Ising universality class, consistent with all available experimental data. We show that, even though the thermodynamic behavior of the system near such a critical point is described by an Ising order parameter, the global conductivity depends on other singular observables and, in particular, the energy density, leading to the emergence of multiple crossover regimes. Finally, we show that in the presence of weak disorder the dimensionality of the system has crucial effects on the size of the critical region that is probed experimentally. ArXiv:0710.1627 and in press at Physical Review Letters. [Preview Abstract] |
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