Session P22: Metal-Insulator Phase Transitions I

Revisiting the Anderson Model with Power-Law Correlated Disorder in 1D and 2D

The dimensionality of a disordered system directly affects the critical energy where a localization/delocalization transition occurs. In non-interacting systems with uncorrelated disorder, it is widely known that all states in one-dimension are localized. However, for some correlations there exist transition energies similar to mobility edges or small subsets of extended states that are robust against disorder. In this talk, we will present results on the diffusion of a wavepacket in a power-law correlated random potential of the form $\langle V(r)V(0) \rangle = \frac{1}{(a+r)^\alpha}$. We also report results for the participation ratio $P_r=\frac{1}{N}\frac{\langle |a_i|^2\rangle^2}{\langle |a_i|^4\rangle}$. Preliminary results for 1D chains support the existence of a mobility edge near the band center. Square and graphene lattices will also be discussed.   

Higher order correction to the RG $\beta $-function for the 3-d Anderson localization transition at unitary symmetry

We have recently calculated the $\beta $-function of the conductance for Anderson Metal-Insulator transition including contributions from the ballistic regime. In three dimensional unitary case, the result of two-loop order diagrams is $\beta $(g)=1-a/g, where a is a constant and g is the dimensionless conductance. However, this result is valid only if there is no diagram with extra diffusons which contributes to the order of 1/g. We show that diagrams with extra diffuson propagators only have higher order contributions in the ballistic regime, which confirms our previous result.   

Singular Behavior of Electronic Eigenstates in the Anderson Model of Localization

We report the observation of a singularity in the electronic properties of the Anderson Model of Localization with diagonal disorder\footnote{P. W. Anderson, Physical Review {\bf 109}, 1492 (1958).} which is clearly distinct from the well- established mobility edge (localization-delocalization transition)\footnote{E. Abrahams, P. W. Anderson, D. C. Licciardello and T. V. Ramakrishnan, Physical Review Letters {\bf 42}, 673 (1979).}$^,$\footnote{For a recent review on Anderson Localization, see Ferdinand Evers and Alexander D. Mirlin, Reviews of Modern Physics {\bf 80}, 1355 (2008).} that occurs in dimensions $d>2$. We present results of numerical calculations for various disorder distributions in dimensions $d$ = $1$, $2$ and $3$, of different properties of the electronic wavefunctions to establish this, and to understand its evolution with disorder distribution, dimension and lattice type. Our data suggest that the model is richer than has been originally believed.   

Temperature dependence of the zero-bias anomaly in the two-site Anderson-Hubbard model

Experiments on disordered strongly correlated electron systems show zero-bias anomalies which are not consistent with either of the two prevailing pictures, by Altshuler and Aronov and by Efros and Shklovskii. Numerical work on the two-dimensional Anderson-Hubbard model shows a zero-bias anomaly with a number of unique features. It has recently been shown that a zero-bias anomaly with many of the same features occurs in an ensemble of two-site Anderson-Hubbard systems. The simplicity of this system allows direct understanding of the mechanism of the anomaly. Here, the temperature dependence of this anomaly is explored. A novel feature is the existence of a temperature driven zero-bias anomaly which appears even in the atomic limit and augments the kinetic energy driven one in the presence of hopping.   

Theoretical perspective on nearly frozen coulomb liquids

Various studies on systems with charge ordered states, such as Wigner crystal, show their extreme fragility resulting from strong frustrations caused by long-range Colulomb-like interactions. Here, a so-called nearly-frozen Coulomb liquid regime is identified featuring a soft Coulomb pseudo-gap with unconventional insulating-like transport. Despite intensive studies, such pseudo-gap regime is still poorly understood. By employing extended dynamical mean field theory (EDMFT) [1] to study a semi-classical lattice gas model of spinless electrons, we successfully demonstrate the existence of such an intermediate liquid regime, and show that the pseudo-gap is, in fact, a general feature for models with long-range interactions. Our analytical results are well supported by exact Monte Carlo calculations. Moreover, we show that standard theories, like self-consistent Gaussian approximation (``spherical model'') and RPA, are ill-suited to describe this interesting regime. The spherical model approach provides the same as EDMFT freezing temperature Tc, but fails to capture the pseudo-gap feature. RPA, however, not only overestimates Tc, but also completely misses the pseudo-gap regime. \\[0pt] [1] S. Pankov and V. Dobrosavljevic, Phys. Rev. Lett. \textbf{94}, 046402 (2005).   

Bound states in the continuum in a multi-electron system

Bound states in a continuum (BIC) occur due to quantum interference of two identical adatoms in a one-dimensional (1D) band. In the past such states have been studied for a one- electron system using several analytical and theoretical methods. We extend the idea of BIC to a multi-electron system. To study this numerically we use the pure Hubbard hamiltoninan and add impurity sites at specific locations. Using this variant of the Hubbard model and an exact diagonalization method we prove that BIC can exist for multi-electron systems. We will also show theoretical proof of such states using the Bethe-Ansatz method   

Spectral functions across the Metal-Insulator transition in the disordered 2D Hubbard model

We study the metal-insulator transition in the repulsive disordered 2D Hubbard model [1,2] using Determinant Quantum Monte Carlo (DQMC). We calculate the spin-spin and current-current correlations to learn about the nature of the conducting and insulating phases. We also obtain local spin-dependent spectroscopic properties, using the maximum entropy method, to understand the role of disorder on the transition in this highly correlated fermion system. We discuss implications of our results for scanning tunneling spectroscopy and dynamical conductivity experiments [3]. \\[4pt] [1]. P.J.H Denteneer, R.T. Scalettar and N. Trivedi, Phys. Rev. Lett.83, 4610 (1999).\\[0pt] [2]. D. Heidarian and N. Trivedi, Phys. Rev. Lett. 93, 126401 (2004).\\[0pt] [3]. M.M. Qazilbash et. al., Science 318, 1750 (2007).   

Time-Correlated Soliton Tunneling in Density Waves

In the quantum sine-Gordon model of a pinned charge or spin density wave, the electrostatic energy generated by charged soliton domain walls leads to a Coulomb blockade threshold electric field for quantum soliton-antisoliton pair creation. This field can be much smaller than the classical depinning field, since the quantum instability occurs as soon as the formerly lowest energy potential well rises to become a metastable well, or ``false vacuum.'' The analogy to time-correlated single electron tunneling and comparison to recent experimental results, as well as broader implications of the proposed tunneling process, are briefly discussed. This work was supported by the State of Texas though the Texas Center for Superconductivity at the University of Houston and the Norman Hackerman Advanced Research Program, and by NIH R21CA133153 and ARRA supplement 3R21CA133153-03S, and by the Robert A. Welch Foundation, and DoE Basic Energy Sciences.   

Level spacing statistics for quantum $k$-core percolation

Quantum percolation is the study of hopping transport of a quantum particle on randomly diluted percolation clusters. Quantum $k$-core percolation is the study of quantum transport on $k$- core percolation clusters where each occupied bond must have at least $k$ occupied neighboring bonds. Within the random phase approximation, we found a random first-order phase transition for the $k$-core conduction transition on the Bethe lattice, and $p_q$, the quantum percolation critical probability, is equal to $p_c$, the geometric percolation critical probability [Phys. Rev. B {\bf 82},104211 (2010)]. To further test this result, we numerically compute the level spacing distribution as a function of occupation probability $p$ and system size. The simulation results provide confirmation for the existence of a discontinuous onset of quantum conduction at $p_q=p_c$.   

The onset of superfluidity of hardcore bosons in disordered ladders

The effect of disorder on the zero-temperature phase diagram of a two-leg ladder of hardcore bosons is investigated using quantum Monte Carlo simulations. We first review some aspects of the clean system which are relevant for the understanding of the disordered case. In the disordered case, an intervening Bose-glass phase between the frozen Mott insulator with zero (or one) bosons per site and the superfluid phase is found. We also investigate the effect of disorder exactly at half filling, where for small values of disorder, there is a commensurate phase with a gap to all excitations, which is eventually destroyed for larger values of disorder. We argue that this phase is always surrounded by the so-called Bose glass and a direct transition from the superfluid is found only in the clean system. Finally, a phase diagram based on our numerical evidence is suggested.   

Global phase diagram of the spinless Falicov-Kimball model in $d = 3$: renormalization-group theory

The global phase diagram of the spinless Falicov-Kimball model in $d = 3$ spatial dimensions is obtained by renormalization-group theory [1]. This global phase diagram exhibits five distinct phases. Four of these phases are charge-ordered (CO) phases, in which the system forms two sublattices with different electron densities. The phase boundaries are second order, except for an intermediate interaction regime, where a first-order phase boundary between two CO phases occurs. The first-order phase boundary is delimited by special bicritical points. The cross-sections of the global phase diagram with respect to the chemical potentials of the localized and mobile electrons, at all representative interaction and hopping strengths, are calculated and exhibit three distinct topologies. The phase diagrams with respect to electron densities are also calculated.\\[4pt] [1] O.S. Sar\i yer, M. Hinczewski, and A.N. Berker, arXiv:1002.1821v1 (2010).   

Improved determination of the self-energy and vertex function in Strong-Coupling Continuous-time Quantum Monte Carlo

The continuous-time quantum Monte Carlo method based on the strong coupling expansion is an efficient and flexible tool for the solution of multiorbital Anderson impurity models. However it is known that it is difficult to accurately compute the intermediate and high-frequency behavior of measured quantities. This leads to large errors, in particular for the self-energy when computed from Dyson's equation. A similar problem occurs for the vertex function when computed directly from the two-particle Green function. We propose an improved way of measuring these quantities, based on higher-order impurity correlation functions. The method yields very accurate estimates for the self-energy and vertex function over the full frequency range. In the segment representation, the improved estimators can be accumulated at essentially no additional computational cost.   

Surface effects in doping a Mott insulator

The physics of doping a Mott insulator is investigated in the presence of a solid-vacuum interface. Using the embedding approach for dynamical mean field theory we show that approaching a Mott insulating phase from the metallic side, a dead layer forms at the surface of the solid, where quasiparticle amplitudes are exponentially suppressed. In particular, we have demonstrated that the reduction of the quasiparticle weight detected by surface sensitive photoemission experiments of a doped Mott insulator are caused by both charge transfer and enhanced correlation effects at the surface. The expected modification of the intra-layer hopping at the surface and inter-layer hopping between the surface and the subsurface layer amplifies the surface effects.   

The Role of the Van Hove Singularity in the Quantum Criticality of the Hubbard Model

A quantum critical point, separating a non-Fermi liquid region from a Fermi liquid, exists in the phase diagram of the Hubbard model [Vidhyadhiraja \emph{et. al}, Phys. Rev. Lett. \textbf{102}, 206407 (2009)]. This quantum critical point is characterized by a vanishing spectral weight and a van Hove singularity (vHS) in the dispersion that crosses the Fermi level. The real part of the critical particle-particle susceptibility exhibits a algebraic decay with temperature, which results in the imaginary part showing scaling at large frequencies. This algebraic decay leads to higher superconducting transition temperatures as compared to the BCS theory, where the pairing susceptibility decays only logarithmically. In this talk, we examine the role of the van Hove singularity in determining this critical behavior. We calculate the bare particle-particle susceptibility of a $d$-wave pair field for the standard two-dimensional tight binding dispersion and for a hypothetical quartic dispersion having ``flatter" or ``extended" singularities. We find that the standard logarithmic vHS cannot correctly describe the critical algebraic behavior and it is essential to have an extended vHS that displays an algebraic singularity. Thus, our results emphasize the possible role of the extended vHS in the unexpectedly higher $T_c$ of cuprates.   

Numerical study of real-time quantum dynamics in spin-electron coupled system

The photo-induced metal-insulator transition is studied by the numerical simulation of real-time quantum dynamics of a double- exchange model. The spatial and temporal evolutions of the system during the transition have been revealed including (i) the threshold behavior with respect to the intensity and energy of light, (ii) multiplication of particle-hole (p-h) pairs by a p-h pair of high energy, and (iii) the space-time pattern formation such as (a) the stripe controlled by the polarization of light, (b) coexistence of metallic and insulating domains, and (c) dynamical spontaneous symmetry-breaking associated with the spin spiral formation imposed by the conservation of total spin for small energy-dissipation rates.