Session T19: Metal-Insulator Transitions I

Sponsoring Units: DCMP
Chair: Nandini Trivedi, The Ohio State University
Room: 321

Thursday, March 21, 2013
8:00AM - 8:12AM

T19.00001: Importance of subleading corrections for the Mott critical point
A.-M.S. Tremblay , Patrick Semon

The interaction-induced metal-insulator transition should be in the Ising universality class. Experiments on layered organic superconductors suggest instead that the observed critical endpoint of the first-order Mott transition in $d=2$ does not belong to any of the known universality classes for thermal phase transitions. In particular, it is found that $\delta=2$. Given the quantum nature of the two phases involved in the transition, we use dynamical mean-field theory and a cluster generalization to investigate whether the new exponents could arise as transient quantum behavior preceding the asymptotic critical behavior. In the cluster calculation, a canonical transformation that minimizes the sign problem in continuous-time quantum Monte Carlo calculations allows previously unattainable precision. Our results show that there are important subleading corrections in the mean-field regime that can lead to an {\it apparent} exponent $\delta=2$. Experiments on optical lattices could verify our predictions for double occupancy. P. S\'emon and A.-M.S. Tremblay, Phys. Rev. B 85, 201101(R)/1-5 (2012).    [Preview Abstract]

Thursday, March 21, 2013
8:12AM - 8:24AM

T19.00002: Quantum critical Mott transition in triangular lattice Hubbard model
Zi Yang Meng , Kuang Shing Chen , Unjong Yu , Shuxiang Yang , Juana Moreno , Mark Jarrell

Using large-scale dynamical cluster quantum Monte Carlo simulations, we study the correlation-driven metal-insulator transition in the half-filled Hubbard model on a triangular lattice, with the interaction strength (U/t) and temperature as control parameters. We compute spectral and transport properties and estimate the Mott transition to occur at the critical interaction strength Uc/t=8.5+/-0.5. From the metallic side, the van Hove singularity in the density of states moves towards the Fermi level with increasing U/t and eventually collapses at the Mott transition, above which the Mott gap opens. In the quantum critical region above the transition point, the system exhibits a marginal Fermi liquid behavior. Due to the competition between electronic correlations and geometric frustrations, we observe non-trivial transport properties across the transition such as a universal jump in the resistivity, consistent with recent quantum field theory proposals. Implications for experiments on the layered triangular lattice organic material k-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2 are also discussed.    [Preview Abstract]

Thursday, March 21, 2013
8:24AM - 8:36AM

T19.00003: Mott criticality in electric transport of triangular lattice Hubbard model
Toshihiro Sato , Kazumasa Hattori , Hirokazu Tsunetsugu

We numerically study electric transport near the Mott metal-insulator transition for the half-filled Hubbard model on a triangular lattice. Our approach is a cellular dynamical mean field theory (CDMFT) with a continuous-time QMC solver and we calculate optical conductivity including vertex corrections. The main issue is the variation of optical conductivity upon controlling Coulomb repulsion $U$ for various temperatures. Near the Mott critical end point, a Drude peak on the metallic side smoothly continues to an ``ingap" peak emerging within the Hubbard gap on the insulating side. We find a critical power-law behavior in their $U$-dependence near the critical point. The obtained critical exponent $1/\delta=0.15$ of the optical weight differs from the exponent $1/\delta=1/3$ of the order parameter (double occupancy) in the CDMFT calculations. This discrepancy suggests that conductivity does not have the same scaling behavior as that for the order parameter[1]. [1]T. Sato, K. Hattori, and H. Tsunetsugu, J. Phys. Soc. Jpn. $\bf 81$, 083703 (2012).    [Preview Abstract]

Thursday, March 21, 2013
8:36AM - 8:48AM

T19.00004: Self-localization of a single hole in Mott antiferromagnets
Zheng Zhu , Hong-Chen Jiang , Yang Qi , Chun-Shun Tian , Zheng-Yu Weng

Anderson localization - quantum suppression of carrier diffusion due to disorders - is a basic notion of modern condensed matter physics. Here, we report a novel localization phenomenon totally contrary to this common wisdom. Strikingly, it is purely of strong interaction origin and occurs without the assistance of disorders. Specifically, by combined numerical (density matrix renormalization group) method and analytic analysis, we show that a single hole injected in a quantum antiferromagnetic ladder is generally self-localized even though the system respects the translational symmetry. The localization length is found to monotonically decrease with the increase of leg number, indicating stronger self-localization in the two-dimensional limit. We find that a peculiar coupling between the doped charge and the quantum spin background causes quantum interference among different hole paths. The latter brings the hole's itinerant motion to a halt, a phenomenological analogy to Anderson localization. Our findings are opposite to the common belief of the quasiparticle picture for the doped hole and unveil a completely new paradigm for lightly doped Mott insulators.    [Preview Abstract]

Thursday, March 21, 2013
8:48AM - 9:00AM

T19.00005: Emergent Metal in Disordered Two Dimensional Mott Insulator
Oinam Nganba Meetei , Nandini Trivedi , Elias Lahoud , Amit Kanigel

We show that disordering a two dimensional Mott insulator leads to an insulator-metal transition, even in the absence of any doping. For disorder strengths comparable to the interaction, the Mott gap closes and extended states develop at the chemical potential. Further increase in disorder drives the emergent metal into a gapless localized insulating phase. We make detailed comparisons of our theoretical predictions on the emergent metal with transport and APRES data on 1T-TaS$_2$ intercalated by Cu. The parent compound 1T-TaS$_2$ is a Mott insulator at low temperature ($T<180K$). In the commensurate charge density wave (CCDW) phase, the ``star of David'' unit cells with 13 Ta atoms form a commensurate triangular lattice with a single half filled band crossing the Fermi energy. Strong interaction produces a Mott gap in the half filled band. Disorder introduced by intercalating Cu atoms between TaS$_2$ layers closes the Mott gap and drives the material into a metallic phase without destroying the CCDW order in good agreement with theory. Our work presents the first evidence of such an insulator-metal transition in a disordered two-dimensional Mott insulator.    [Preview Abstract]

Thursday, March 21, 2013
9:00AM - 9:12AM

T19.00006: Configuration Interaction as an Impurity Solver: Benchmark Dynamical Mean-Field Theory for the Hubbard Model
Ara Go , Andrew J. Millis

The configuration interaction technique has been widely used in quantum chemistry to solve quantum many body systems with lower computational costs than exact diagonalization and was introduced by Dominika Zgid, Emanuel Gull, and Garnet Kin-Lic Chan [Phys. Rev. B \textbf{86}, 165128 (2012)] as a solver for the impurity models of dynamical mean field theory. We extend their work, demonstrating for the one and two dimensional Hubbard model how the method reproduces the known results and allows convergence with bath size to be studied in cluster dynamical mean field theory. As an example of the power of the method, cluster dynamical mean field studies of the three band copper-oxygen model are presented.    [Preview Abstract]

Thursday, March 21, 2013
9:12AM - 9:24AM

T19.00007: Periodic Anderson model with Holstein phonons on the conduction band
Peng Zhang , Pete Reis , Ka-Ming Tam , Mark Jarrell , Juana Moreno , Fakher Assaad , Andy McMahan

The volume collapse of Cerium is a long standing problem in condensed matter physics. Recent interest has been attracted to this problem by the experimental discovery that lattice vibrations play an important role in the entropy change of such a first-order phase transition. Using Continuous Time Quantum Monte Carlo as impurity solver of Dynamical Mean Field Theory, the Periodic Anderson Model with Holstein phonons coupling to the conduction band is investigated. Above a certain electron-phonon coupling, we find two coexisting phases separated by a first order transition line, which ends at a second order terminus. One of the coexisting phases is a Kondo Singlet phase with polaronic features while another is local moment phase with bipolaronic features.    [Preview Abstract]

Thursday, March 21, 2013
9:24AM - 9:36AM

T19.00008: Spontaneuous symmetry breaking in matrix models
Fabio Franchini

Matrix models with rotational invariant weights provide, in the large $N$ limit, a robust universality of correlated eigenvalues. Here, we want to argue that a weight that breaks the eigenvalue distribution into disjoint supports, further induces a spontaneous breaking of the rotational symmetry. This SSB of the $U(N)$ can potentially be used as a toy model to study the eigenstate distribution at the Anderson Metal/Insulator Transition.    [Preview Abstract]

Thursday, March 21, 2013
9:36AM - 9:48AM

T19.00009: Solving a puzzle in the Anderson transition with long-range correlated potentials
Greg Petersen , Nancy Sandler

The conditions for an Anderson transition in 1D systems has been an open question since it's discovery a half century ago. Although scaling theory predicts localization in this case, it has been shown that a transition exists in the presence of some form of long-range correlations in the on-site energies. One of the most widely used examples are disorder potentials generated by $1/k^\alpha$ spectral densities [1] that, with an appropriate short range cutoff, result in vanishing correlation functions in the thermodynamic limit. However, these results are in direct contradiction to work by Kotani et. al. [2] that argues for the existence of a metallic state only when infinite range correlations are non-zero. In this talk we will show that there is no contradiction between the two results as the correlation function generated from numerical techniques is staunchly different from analytic expectations. Furthermore, we will present the exact analytic expression for the correlation function in the thermodynamic limit. Finally, we will discuss the role played by short- and long-range features of the correlation function in the Anderson transition. \\[4pt] [1] F. Moura and M. Lyra, PRL {\bf 81}, 3735 (1998)\\[0pt] [2] S. Kotani and B. Simon Commun. Math. Phys. {\bf 112},103 (1985).    [Preview Abstract]

Thursday, March 21, 2013
9:48AM - 10:00AM

T19.00010: Momentum Space Signatures of Anderson Localization
Conrad Moore , Chinedu Ekuma , Hanna Terletska , Ziyang Meng , Juana Moreno , Mark Jarrell

The ensemble averaged density of states is commonly used as an order parameter to distinguish between a metal and insulator. However, for disordered electronic systems this is not the case: the disorder averaged density of states exhibits no singular behavior as the mobility edge between extended and localized states is crossed. In addition, recent work on rare events in the Anderson model further complicate this characterization with ``resonant states'' becoming significant in the tails of the density of states. In this work, we present exact diagonalization results of the Anderson model and review two quantities that measure the localization transition: the inverse participation ratio and the typical (geometrically averaged) density of states. We also examine the log-normal distribution of the local density of states in real and momentum space. In particular, the results in momentum space provide a justification for the systematic extension of the single site typical medium theory to a momentum coarse grained Dynamical Cluster Approximation where the non-local effects can be included systematically.    [Preview Abstract]

Thursday, March 21, 2013
10:00AM - 10:12AM

T19.00011: Anderson localization in one-dimension with Levy-type disorder
David Mayett , Jennifer Schwarz

Abstract: Quantum transport through disordered systems has been the subject of extensive research since Anderson's seminal theory of localization. Motivated by experimental realizations of light transport across media exhibiting Levy-type fluctuations, we study the one-dimensional Anderson model where the random site energies are governed by a probability distribution with a broad tail, otherwise known as Levy-type. We numerically compute the Lyapunov exponent and its variance. This exponent is a self-averaging quantity whose inverse in certain cases can be used to define the localization length. Furthermore, we check for the validity of single parameter scaling (SPS), and its dependence on the Levy index.    [Preview Abstract]

Thursday, March 21, 2013
10:12AM - 10:24AM

T19.00012: Interactions produce strongly non-Gaussian spatial correlations of the screened random potential
H. Javan Mard , E.C. Andrade , E. Miranda , V. Dobrosavljevi\'c

We perform variational studies of the interaction-localization problem\footnote{V. Dobrosavljevi\'c, N. Trivedi, and J. M. Valles Jr, {\em Conductor Insulator Quantum Phase Transitions} (Oxford University Press, UK, 2012).}, by using both the Hartree-Fock and the Gutzwiller (slave boson) approximations to describe the interaction-induced renormalizations of the effective (screened) random potential seen by quasiparticles. Here we present results of careful finite-size scaling studies for the conductance of disordered Hubbard chains at half-filling and zero temperature. While our results indicate that quasiparticle wavefunctions remains exponentially localized even in presence of moderate to strong repulsive interactions, we find surprisingly strong enhancement of the conductance of finite size systems. In particular, we show that interactions produce a strong decrease of the characteristic conductance scale $g^*$ signaling the onset of strong localization. We show that this effect, which cannot be captured by a simple renormalization of the disorder strength, instead reflects a peculiar \textit{non-Gaussian form for the spatial correlations} of the screened disordered potential, a so-far neglected mechanism to suppress the role of Anderson localization (interference) effects.    [Preview Abstract]

Thursday, March 21, 2013
10:24AM - 10:36AM

T19.00013: Verwey Metal-Insulator Transition in Magnetite from the Slave-Boson Approach
Mohammad Sherafati , Sashi Satpathy , Dix Pettey

We study the Verwey metal-insulator transition in magnetite (Ref.1) by solving a three-band extended Hubbard Hamiltonian for spinless fermions using the slave-boson approach, which also includes coupling to the local phonon modes. This model is suggested from the earlier density-functional studies of magnetite.(Ref.2) We first solve the 1D Hubbard model for the spinless fermions with nearest-neighbor interaction by both Gutzwiller variational and slave-boson methods and show that these two approaches yield different results unlike in the case of the standard Hubbard model, thereby clarifying some of the discrepancies in the literature (Ref.3), then we extend the formalism to three-band Hamiltonian for magnetite. The results suggest a metal-insulator transition at a critical value for the intersite interaction.\\ References:\\ 1) E.J.W. Verwey, Nature 144, 327 (1939)\\ 2) Z. Zhang and S. Satpathy, Phys. Rev. B 44, 13319 (1991) \\ 3) P. Fazekas, Solid State Communications 10, 175 (1972); Physica Scripta, T29, 125 (1989); G. Seibold and E. Sigmund, Z. Phys. B 101, 405 (1996)    [Preview Abstract]

Thursday, March 21, 2013
10:36AM - 10:48AM

T19.00014: Thoery of Charge Order and Heavy-Electron Formation in the Mixed-Valence Compound KNi$_2$Se$_2$
James Murray , Zlatko Tesanovic

The material KNi$_2$Se$_2$ has recently been shown to posses a number of striking physical properties, many of which are apparently related to the mixed valency of this system, in which there is on average one quasi-localized electron per every two Ni sites. The material exhibits a charge density wave (CDW) phase that disappears upon cooling, giving way to a low-temperature coherent phase characterized by an enhanced electron mass, reduced resistivity, and an enlarged unit cell free of structural distortion. Starting from an extended periodic Anderson model and using the slave-boson formulation, we develop a model for this system and study its properties within mean-field theory. We find a reentrant first-order transition from a CDW phase, in which the localized moments form singlet dimers, to a heavy Fermi liquid phase as temperature is lowered. The magnetic susceptibility is Pauli-like in both the high- and low-temperature regions, indicating the absence of free local moments, which are typically present in heavy-fermion materials at temperatures above the coherence temperature.    [Preview Abstract]