Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session G47: Metal-Insulator and Other Electronic Phase Transitions: Theory |
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Sponsoring Units: DCMP Chair: Andre-Marie Tremblay, Universite de Sherbrooke Room: Mile High Ballroom 4F |
Tuesday, March 4, 2014 11:15AM - 11:27AM |
G47.00001: Charge-Spin Mutual Frustration in Hubbard Model and Quantum Phase Diagram Long Zhang, Zheng-Yu Weng The charge-spin mutual frustration shapes the electron and spin correlations in the moderate coupling regime of the Hubbard model. We propose that it can be captured by the mutual semion statistics between chargons and spinons, i.e., they view each other as $\pm \pi$ gauge fluxes. Gapless spin liquid phases emerge on a square lattice with a $\pi$-flux in each plaquette and an anisotropic triangular lattice, consistent with numerical simulations and experiments on the organic material EtMe$_3$Sb[Pd(dmit)$_2$]$_2$. We find that the quasiparticle decoherence due to severe phase fluctuations can cause Mott transition without fully suppressing charge fluctuations, suggesting the concept of ``weak Mott insulators.'' [Preview Abstract] |
Tuesday, March 4, 2014 11:27AM - 11:39AM |
G47.00002: The nature of quantum criticality in the Hubbard model on honeycomb lattice Igor Herbut, Fakher Assaad Hubbard model on graphene's honeycomb lattice at the filling one half and at zero temperature exhibits the semi-metallic phase at weak coupling, and the insulating Neel ordered phase at strong coupling. The nature of the phase transition between these two phases has been a contentious issue in literature. We will present evidence from recent quantum Monte Carlo calculations in favor of the direct, continuous transition, without an intermediate spin-liquid phase. Both the staggered magnetization and the single-particle gap display excellent finite-size scaling, with the same scaling function, and with the critical exponents which are in accord with the dimensional expansion that was devised for the problem near three spatial dimensions. We will discuss the effective Gross-Neveu-Yukawa low-energy theory for this quantum phase transition, with the new ``fermionic'' critical point, at which Dirac fermions are fully coupled, and cannot be simply ``integrated out''. Some new universal amplitudes which characterize this interesting phase transition with massless excitations on both sides will be mentioned. References: F. Assaad and I. F. Herbut, Physical Review X, vol. 3, 031010 (2013); I. F. Herbut, V. Juricic, and O. Vafek, Physical Review B, vol. 80, 075432 (2009). [Preview Abstract] |
Tuesday, March 4, 2014 11:39AM - 11:51AM |
G47.00003: The effect of geometric frustration on the charge and spin correlations of the 2D Hubbard model near the metal-insulator transition Matthew Enjalran We investigate the effect of geometric frustration on the low temperature charge and spin correlations of interacting electrons on the triangular and kagome lattices near the metal-insulator transition. We consider the half-filled single band Hubbard model in the unrestricted Hartree-Fock approximation and study the evolution of the low temperature phases on each lattice as function of geometric frustration, which is achieved by tuning the ratio of the hopping parameters $t^{\prime}/t$. We present results for the mean-field phase diagram of the anisotropic triangular lattice as the relative hopping strength changes the lattice topology from the square lattice to the fully frustrated triangular lattice to weakly coupled chains. Preliminary results for mean-field phases on the anisotropic kagome lattice are also presented. [Preview Abstract] |
Tuesday, March 4, 2014 11:51AM - 12:03PM |
G47.00004: Mott-Hubbard vs Charge-Transfer Insulating Behavior in the CuO$_2$ Plane Giovanni Sordi, Patrick Semon, A.-M. S. Tremblay High temperature superconductivity emerges in the CuO$_2$ plane upon doping a Mott insulator. The Mott insulating state occurs in different regimes, Mott-Hubbard insulator and charge-transfer insulator. The latter is relevant especially for hole-doped cuprates. Within a three-band model we can explore both charge-transfer and Mott-Hubbard systems. Here we study the metal-insulator transitions in a three-band copper oxide model within cluster dynamical mean-field theory with continuous-time quantum Monte Carlo as an impurity solver. As a function of doping, charge-transfer energy and interaction strength, the normal state of this model shows the two types of metal-insulator transitions, metal to charge-transfer insulator and metal to Mott-Hubbard insulator. [Preview Abstract] |
Tuesday, March 4, 2014 12:03PM - 12:15PM |
G47.00005: Spatial Correlation in the Three-band Copper Oxide Model: Dynamical Mean-field Study with Configuration Interaction Based Impurity Solver Ara Go, Andrew J. Millis The three-band copper oxide model is studied using the single-site and four-site dynamical mean-field theory with configuration interaction based impurity solver. Comparison of the single and four site approximations shows that short ranged antiferromagnetic correlations are crucial to the physics. In the undoped case, they increase the gap size, shift the metal-insulator phase boundary and enhance the conductivity at the gap edge. The relation of antiferromagnetism and the pseudogap is discussed for the doped case. The new solver permits the inclusion of more bath orbitals which are crucial for accurate studies of spectral properties near the gap edge. [Preview Abstract] |
Tuesday, March 4, 2014 12:15PM - 12:27PM |
G47.00006: Mottness-induced healing in strongly correlated superconductors S. Tang, V. Dobrosavljevi\'c, E. Miranda We study impurity healing effects in models of strongly correlated superconductors. We show that in general both the range and the amplitude of the spatial variations caused by nonmagnetic impurities are significantly suppressed in the superconducting as well as in the normal states. We explicitly quantify the weights of the local and the non-local responses to inhomogeneities and show that the former are overwhelmingly dominant over the latter. We find that the local response is characterized by a well-defined healing length scale, which is restricted to only a few lattice spacings over a significant range of dopings in the vicinity of the Mott insulating state. We demonstrate that this healing effect is ultimately due to the suppression of charge fluctuations induced by Mottness. We also define and solve analytically a simplified yet accurate model of healing, within which we obtain simple expressions for quantities of direct experimental relevance, such as the healing length. [Preview Abstract] |
Tuesday, March 4, 2014 12:27PM - 12:39PM |
G47.00007: Effects of Hund's coupling on the Mott transition in multiorbital systems Aaram Joo Kim, Gun Sang Jeon, MooYoung Choi We study the phase transitions in the two-orbital Hubbard model having different orbital bandwidths, with emphasis on the effects of the Ising-type Hund's coupling. Within the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method, we confirm the existence of a non-Fermi-liquid for intermediate interactions. In contrast to the paradigmatic Mott transition in the single-band Hubbard model, a metallic phase is dominant over a localized Mott insulator at finite temperatures, resulting in the opposite slope of the phase boundary. We also investigate how the nature of the Mott transition between the non-Fermi liquid and the Mott insulator is affected by the variations in the Hund's coupling strength. [Preview Abstract] |
Tuesday, March 4, 2014 12:39PM - 12:51PM |
G47.00008: Phase separation in doped Mott insulators Chuck-Hou Yee, Leon Balents Motivated by the commonplace observation of Mott insulators away from integer filling, we construct a simple thermodynamic argument for phase separation in first-order doping-driven Mott transitions. The theory predicts the transition is percolative and should exhibit Coulomb frustration. As an application, we consider the titanate family of perovskites, an ideal test case since both the doping and correlation strength can be tuned. We compute the critical dopings required to drive the Mott transition using first-principles methods combined with dynamical mean-field theory, finding good agreement with experiment. [Preview Abstract] |
Tuesday, March 4, 2014 12:51PM - 1:03PM |
G47.00009: Random Field Driven Spatial Complexity at the Mott Transition in Vanadium Dioxide Shuo Liu, Benjamin Phillabaum, Erica Carlson, Karin Dahmen, Mumtaz Qazilbash, Dimitri Basov, Vidhyadhiraja Sudhindra Scanning near-field infrared microscopy on vanadium dioxide (VO$_2$) reveals the complex pattern formation associated with the temperature driven metal-insulator transition [1]. We apply recently developed cluster techniques [2] to the observed multiscale patterns of inhomogeneous local conductivity, quantifying the statistics of the sizes and shapes of the geometric metallic and insulating clusters through several measures characterized by critical exponents in the power law scaling, such as the cluster size distribution $\tau$, volume fractal dimension $d_v$ and hull fractal dimension $d_h$. These quantitative measures show power-law behavior over multiple decades, and the values of the extracted critical exponents indicate that the Mott critical end point is in the universality class of the random field ising model, revealing a delicate interplay between interactions and disorder in the material. The cluster techniques employed here can readily be applied to 2D image data in the context of other strong correlated systems and microscopy techniques for the study of critical behavior.\newline \par \noindent [1] M. M. Qazilbash {\it et al.}, {\it Science} {\bf 318}, 1750 (2007).\newline [2] B. Phillabaum, E. W. Carlson, and K. A. Dahmen, {\it Nat. Commun.} {\bf 3}, 915 (2012). [Preview Abstract] |
Tuesday, March 4, 2014 1:03PM - 1:15PM |
G47.00010: Nature of the Mott transition in the one- and two-dimensional Hubbard models Masanori Kohno The relationship between the single-particle excitation in the metallic phase and the spin excitation in the Mott insulating phase is discussed, based on the results for the one- and two-dimensional Hubbard models obtained by using the Bethe ansatz, dynamical density-matrix renormalization group method, and cluster perturbation theory [1,2]. By noting that the dispersion relation of the single-particle excitation in the zero-doping limit is directly related to that of the spin-wave excitation of the Mott insulator and that the spectral weight of the single-particle excitation in the electron addition spectrum gradually disappears toward the Mott transition, the nature of the Mott transition can be considered as freezing of the charge degrees of freedom, reflecting the spin-charge separation in the Mott insulator [1,2]. This feature is contrasted with the feature of a Fermi liquid and that of the transition between a band insulator and a metal. \\[4pt] [1] M. Kohno, Phys. Rev. Lett. 105, 106402 (2010). \\[0pt] [2] M. Kohno, Phys. Rev. Lett. 108, 076401 (2012). [Preview Abstract] |
Tuesday, March 4, 2014 1:15PM - 1:27PM |
G47.00011: Effect of electron-electron interactions on density of states singularities found in the Anderson model Rachel Wortis, Jayanayana Perera After Anderson first predicted localization in 1958, significant effort went into demonstrating that there is no singularity in the density of states associated with the mobility edge. It therefore came as a surprise when Johri and Bhatt[PRL {\bf 109} 076402 (2012)] recently uncovered the existence of a non-analyticity in the density of states near the band edge for systems with bounded disorder, in an energy range outside that captured by previous work. Moreover, they found that the singularity marks a transition to an energy range in which the DOS contributions come primarily from resonant states: states associated with clusters of sites of similar potential. While the work of Johri and Bhatt considers the traditional Anderson model without electron-electron interactions, there is currently significant interest in the effect of interactions on disordered systems. We therefore explore the effect a Hubbard $U$ interaction on the DOS feature found by Johri and Bhatt. We find that the original singularity persists at low values of $U$ but loses its sharpness at intermediate values, while new singularities associated with different types of resonance appear elsewhere in the spectrum. [Preview Abstract] |
Tuesday, March 4, 2014 1:27PM - 1:39PM |
G47.00012: Landau theory of Anderson localization and STM spectra in $Ga_{1-x} Mn_x As$ S. Mahmoudian, V. Dobrosavljevic, E. Miranda The recently developed Typical Medium Theory\footnote{V. Dobrosavljevi\'c, Int. J. Mod. Phys. B {\bf 24}, 1680 (2010).} provides the conceptually simplest order parameter description of Anderson localization by self-consistently calculating the geometrically-averaged (typical) local density of states (LDOS). Here we show how spatial correlations can also be captured within such a self-consistent theory, by utilizing the standard Landau method of allowing for (slow) spatial fluctuations of the order parameter, and performing an appropriate gradient expansion. Our theoretical results provide insight into recent STM experiments, which were used to visualize the spatially-fluctuating electronic wave functions near the metal insulator transition in $Ga_{1-x} Mn_x As$.\footnote{A. Richardella {\em et al.}, Science {\bf 327}, 665 (2010).} We show that, within our theory, all features of the experiment can be accounted for by considering a model of disorder renormalized by long-range Coulomb interactions. This includes the pseudogap formation, the $C(R)\sim 1/R$ form of the LDOS autocorrelations function, and the $\xi \sim 1/E$ energy dependence of the correlation length at criticality. [Preview Abstract] |
Tuesday, March 4, 2014 1:39PM - 1:51PM |
G47.00013: Strong disorder renormalization group study of Anderson localization H. Javan Mard, V. Dobrosavljevi\'c, J.A. Hoyos, E. Miranda We formulate a Strong Disorder Renormalization Group (SDRG) approach, to investigate $1D$ tight-binding models with simultaneous presence of random site energies and random hopping elements. We show that the beta function (describing the scaling properties of the conductance) can, under certain conditions, be obtained from an analytical solution of the appropriate SDRG flow equations, and we find excellent agreement with the results obtained from (numerically) exact transfer matrix calculations. We also show that, for the purposes of calculating the conductance, current conservation assures that the SDRG decimation represents an exact procedure for any amount of disorder. Our study demonstrates that the particle-hole symmetric model (no site disorder) represents an unstable but universal fixed point of the SDRG flows. In contrast, for the generic model where both disorder types are present, the system flows toward a {\em line of fixed points}, corresponding to different amounts initial (site) disorder, thus implying a non universal form of the beta function. [Preview Abstract] |
Tuesday, March 4, 2014 1:51PM - 2:03PM |
G47.00014: Dynamics close to the many-body localization transition Yevgeny Bar Lev (Krivolapov), David R. Reichman It has recently been suggested that in a generic class of disordered and (short-ranged) interacting quantum systems a dynamical metal-insulator transition may occur at finite temperatures. This proposed phenomenon is called many-body localization (MBL). In this work we study the real-time dynamics of this transition for a range of parameters where the transition should manifest according to theory and recent numerical studies. For this purpose, we numerically solve the non-equilibrium quantum kinetic equations in the self-consistent second-Born approximation, the same approximation used in the original prediction of MBL. For accessible times, we observe a complex sequence of dynamical regimes. Surprisingly we find little change of behavior upon crossing the putative dynamical phase boundary as determined by previous numerical studies. [Preview Abstract] |
Tuesday, March 4, 2014 2:03PM - 2:15PM |
G47.00015: Asymptotically Exact Scenario of Strong-Disorder Criticality in One-Dimensional Superfluids Lode Pollet, Nikolay Prokof'ev, Boris Svistunov We present a controlled rare-weak-link theory of the superfluid-to-Bose/Mott glass transition in one-dimensional disordered systems. The transition has Kosterlitz-Thouless critical properties but may occur at an arbitrary large value of the Luttinger parameter $K$. In contrast to the scenario by Altman {\it et al.} [Phys. Rev. B {\bf 81}, 174528 (2010)], the hydrodynamic description is valid under the correlation radius and defines criticality via the renormalization of microscopically weak links, along the lines of Kane and Fisher [Phys. Rev. Lett. {\bf 68}, 1220 (1992)]. The hallmark of the theory is the relation $K^{(c)}=1/\zeta$ between the critical value of the Luttinger parameter at macroscopic scales and the microscopic (irrenormalizable) exponent $\zeta$ describing the scaling $\propto 1/N^{1-\zeta}$ for the strength of the weakest link among the $N/L \gg 1$ disorder realizations in a system of fixed mesoscopic size $L$. [Preview Abstract] |
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