Conference: Thursday February 12 to Saturday February 14, 2015

• Philip Adams, Louisiana State University, USA

  Hysteresis, Avalanches, and Slow Relaxation: Complex non-equilibrium spin dynamics in a Zeeman-limited superconductor
  We have recently been studying non-equilibrium spin dynamics of BCS superconductivity in a high Zeeman field. Thin aluminum films are driven from the superconducting phase to the normal phase by the application of a magnetic field that is oriented parallel to the film surface. Near the first-order parallel critical field transition, we observe avalanches in both transport and density of states measurements. These avalanches are not associated with flux jumps but are representative of the behavior of the condensate as the system tries to accommodate spin-singlet superconductivity in the presence of a large Zeeman field and disorder. I will argue that the presence of avalanches in the density of state spectra has important implications for the nature of the superconducting ground state near the Clogston-Chandrasekhar limit. Specifically, we believe that a non-trivial, spatially modulated, order parameter emerges in the critical regime.

• Kieron Burke, University of California, Irvine, USA

  Why strong correlation is difficult in density functional theory
  This talk will summarize a variety of work on strongly correlated systems, testing and understanding failures of the density functional theory (DFT). I begin with an illustration of DFT on the simplest possible system, a two-site Hubbard problem [D. J. Carrascal, J. Ferrer, J. C. Smith, and K. Burke, in prep.]. This is used to show how DFT works and its differences from traditional many-body approaches. Then I will show the importance of moving from lattice Hamiltonians to real-space (i.e., continuum) descriptions [Phys. Rev. Lett. 109, 056402 (2012)]. I will describe a number of papers[Phys. Chem. Chem. Phys. 14, 8581 - 8590 (2012); Phys. Rev. Lett. 111, 093003 (2013); Phys. Rev. B 90, 045109 (2014)] in collaboration with Steve White in which DMRG calculations are used to solve one dimensional systems exactly, and compared to essentially exact DFT and to approximate DFT. I will discuss our latest results in this area, and ask for ideas on directions to go in.

• Randy S. Fishman, Oak Ridge National Laboratory, USA

  Using inelastic scattering measurements to determine the complex spin states of multiferroic materials
  Because they couple magnetic and electric degrees of freedom, multiferroic materials hold tremendous technological promise and remain the subject of intense scrutiny. In practice, elastic neutron scattering alone is insufficient to determine the complex, non-collinear spin structures of these materials. But inelastic spectra provide dynamical "fingerprints" for the spin states and interactions of multiferroic materials. This is demonstrated for two materials that fall within different classes of multiferroics. Whereas BiFeO₃ is a type I multiferroic with the ferroelectric transition temperature Tc higher then the Néel transition temperature TN, CuFeO₂ is a type II multiferroic with T_c = TN. Although the spin states of these materials are distorted cycloids or spirals, there are important differences between the two due to the different origins of their multiferroic behavior. I also discuss the computational challenges posed by solving the inelastic spectra for materials with very large unit cells, such as the type II multiferroic MnWO₄. Research sponsored by the Division of Materials Sciences and Engineering, U.S. Department of Energy under contract with UT-Battelle, LLC.

• Hartmut Hafermann, Institut de Physique Théorique, CEA, France

  Collective charge excitations of strongly correlated electrons, vertex corrections and gauge invariance
  The collective, long wavelength charge excitations in correlated media are considered in presence of short and long range forces. As an example for the case of a short range interaction, the two-dimensional Hubbard model is examined within dynamical mean-field theory (DMFT). It is shown that the DMFT susceptibility including vertex corrections respects the Ward identity and yields a manifestly gauge invariant response in finite dimensions [Phys. Rev. B 90, 235105 (2014)]. A zero-sound mode is found as expected for short range forces. The relation between the vertex corrections, gauge invariance and the appearance of the collective modes is discussed. Long range forces are treated within extended dynamical mean-field theory (EDMFT). In order to obtain a gauge invariant response and a proper description of the plasmons in this case, it is necessary to additionally incorporate some non-local vertex corrections into the polarization. This may be achieved by means of the dual boson approach. It is shown that correlations induce a spectral weight transfer and renormalization of the dispersion in the two-particle spectra [Phys. Rev. Lett. 113, 246407 (2014)]. These effects are reminiscent of interaction induced changes found in single-electron spectra in correlated media. Finally, the role of the polarization corrections for the charge-ordering transition in the extended Hubbard model is discussed [Phys. Rev. B 90, 235135 (2014)].

• Václav Janiš, Academy of Sciences, Czech Republic & Louisiana State University

  Parquet equations for disordered and interacting electron systems: Self-energy and the role of the Ward identity.
  I introduce a way how to choose the one-electron Green functions in the parquet equations for two-particle vertices so that to reach qualitative thermodynamic consistency. Parquet equations for disordered and interacting electron systems are discussed separately. In the former case I show how to use the parquet equations in the construction of the two-particle vertex being compatible with the Ward identity. In the latter case I use a linearized Ward identity in the external magnetic field to introduce a thermodynamic self-energy that is then used in the one-electron Green's functions of the parquet equations. The role and significance of the Schwinger-Dyson equation in such a formulation of the parquet equations are explained.

• Ehsan Khatami, San José State University, USA

  Numerical Linked-Cluster Expansion Approach for Strongly-Correlated Electronic Systems
  Recent advances in computational methods for strongly-correlated electronic systems have helped us not only with the ability to simulate more realistic models and achieve lower temperatures, but also in gaining a better control and even eliminating sources of error and approximations. In this talk, I will introduce the numerical linked-cluster expansion (NLCE), a novel and highly-parallelizable technique for quantum lattice models and discuss its advantages and disadvantages over some of the more popular methods that rely on quantum Monte Carlo algorithms. NLCEs combine two powerful techniques, namely, high-temperature series expansions and the exact diagonalization to provide highly-precise finite-temperature properties of the model directly in the thermodynamic limit. As an example, I will focus on the applications of NLCEs to the Fermi-Hubbard model and show results for the thermodynamic properties, including magnetic and superconducting correlations, of the model on several different geometries. Comparisons to results from the determinantal quantum Monte Carlo will be presented for select cases.

• Erik Koch, German Research School for Simulation Sciences, Jülich, Germany

  Stochastic sampling for the analytic continuation of imaginary-time data
  tochastic sampling methods solve an inverse problem, e.g., reconstructing the spectral function from imaginary-time data obtained in QMC simulations, by averaging all admissible solutions with a weight given by how well they reproduce the data. They are appealing, as they appear unbiased and thus have the potential to resolve sharp features in the spectral function. Discretizing the inverse problem to make numerical calculations possible we have, however, to introduce a parametrization of the real-axis that acts like a default model, i.e., determining the result in the absence of data. We discuss how the effect of this default model depends on the number of points in the real-axis grid. To make this analysis possible, we (i) introduce an efficient stochastic sampling algorithm, blocked mode sampling, based on the singular-value decomposition of the discretized integral kernel, and (ii) derive how the stochastic processes for different discretizations are related. Finally we give a recipe for constructing real-axis grids for practical calculations.

• Wei Ku, Brookhaven National Laboratory, USA

  Connecting real materials to low-energy effective Hamiltonian: applications of symmetry-respecting Wannier functions
  This talk will cover the basics of capturing the realistic aspects of materials by using symmetry-respecting Wannier functions. Specifically, low-energy effective Hamiltonian can be obtained (so-called down-folding) for various purposes, including further analysis of density functional theory and many-body treatment of one-particle and two-particle excitations. The talk will also include recent development in treating disordered impurities and propagation of excitations.

• Salvatore R. Manmana, Universität Göttingen, Germany

  Matrix product state formulation of frequency-space dynamics at finite temperatures
  I will present a flexible density-matrix renormalization group approach to calculate finite-temperature spectral functions of one-dimensional strongly correlated quantum systems. The method combines the purification of the finite-temperature density operator with a moment expansion of the Green's function. Using this approach, we study finite-temperature properties of dynamical spectral functions of spin-1/2 XXZ chains with Dzyaloshinskii-Moriya interactions in magnetic fields and analyze the effect of these symmetry breaking interactions on the nature of the finite-temperature dynamic spin structure factor.

• Frank Marsiglio, University of Alberta, Canada

  The Dynamic Hubbard Model: studies with DMFT and exact diagonalization
  Strong correlations play an important part of all superconductors. Many of these correlations are described through a competition between kinetic energy processes and potential energy considerations. In the Dynamic Hubbard model these two considerations become somewhat blurred. We describe various effective models where the role played by hole-like quasiparticles becomes very distinct from that of their electron-like counterparts.

• Luca de' Medici, European Synchrotron Radiation Facility, Grenoble, France

  Slave-spin mean-field calculations, an essential dynamical multi-orbital mean-field: application to Iron superconductors
  Slave-variable mean fields have a long history in condensed matter theory, slave bosons being a most known example. They enable a non-perturbative treatment of interacting many-body fermions and, in their simplest mean-field for Hubbard-like models to minimally treat the local dynamical fluctuations generating the mass enhancement caused by electronic correlations, for instance. The slave-spin mean field is a very convenient implementation that allows to easily tackle multi-orbital systems at a very cheap computational cost. Successes of this method include realistic studies of the recently discovered iron superconductors, that will be illustrated.

• Rudolf Roemer, University of Warwick, United Kingdom

  Self-assembling tensor networks and holography in disordered spin chains
  We show that the numerical strong disorder renormalization group algorithm of Hikihara et al. [Phys. Rev. B 60, 12116 (1999)] for the one-dimensional disordered Heisenberg model naturally describes a tree tensor network (TTN) with an irregular structure defined by the strength of the couplings. Employing the holographic interpretation of the TTN in Hilbert space, we compute expectation values, correlation functions, and the entanglement entropy using the geometrical properties of the TTN. We find that the disorder-averaged spin-spin correlation scales with the average path length through the tensor network while the entanglement entropy scales with the minimal surface connecting two regions. Furthermore, the entanglement entropy increases with both disorder and system size, resulting in an area-law violation. Our results demonstrate the usefulness of a self-assembling TTN approach to disordered systems and quantitatively validate the connection between holography and quantum many-body systems [Phys. Rev. B 89, 214203 (2014)].

• Alexey Rubtsov, Moscow State University & Russian Quantum Center, Russia

  Towards a numerically exact description of correlated open quantum systems
  A description of the dynamics of a correlated quantum system coupled to a bath remains a major challenge for the community. The most remarkable progress has been achieved for an equilibrium state, when continuous-time Quantum Monte Carlo schemes deliver a good accuracy for realistic multiorbital impurity problems. We will discuss state-of-art algorithms, as well as approximate schemes that allow to reduce the description of correlated media to a multiorbital impurity problem -- in particular, Dynamical Mean Field theory and dual-fermion formalism. The calculation of real-time dynamics is much more complicated, primary because of a limited applicability of the stochastic schemes. Some understanding can be obtained operating with a simplified bath operators. An assumption that the bath is Markovian leads to Lindblad formalism and similar schemes. We will consider how the Lindblad term should be modified for a correlated system coupled to a non-vacuum bath, and present our results for a metastability of the decay dynamics of a frustrated correlated system. We believe that our theory can be used for a practical calculation of the metastability effects in nanodevices, catalysis etc. A special attention will be paid to the scalability of the algorithms, to check out where the use of petascale systems can result in a breakthrough.

• Ka-Ming Tam, Louisiana State University, USA

  Simulations of Edwards-Anderson model using GPU
  Monte Carlo simulations of the Ising model and its variants play an important role in the computational physics, and they have helped the discovery of many important physics phenomena over the past few decades. Unfortunately, the existence and nature of spin glass due to random disorder still remains as open questions. A main obstacle in Monte Carlo simulations of random frustrated systems is the long relaxation time. Developing an efficient parallel implemen- tation on state-of-the-art computation platforms is highly desirable. The Graphics Processing Unit (GPU) is such a platform that provides an opportunity to significantly enhance the computational performance. In this talk, we present optimization and tuning approaches for the CUDA implementation of the spin glass simulation on GPUs. We discuss the integration of various design alternatives, such as GPU kernel construction with minimal communication, memory tiling, and look-up tables. We present a binary data format, and introduce the Compact Asynchronous Multi-spin Coding (CAMSC), which provides an additional speedup compared with the traditionally used Asynchronous Multispin Coding. We employ the GPU code to calculate an indicator composed of the ratio of susceptibilities at finite wavenumbers, which has been recently proposed to avoid the difficulties in the finite size scaling of a zero momentum quantity. This new indicator is rather noisy, the GPU implementation facilitates the generation of a large pool of samples at low temperature to reduce the the noise.

• Karen Tomko, Ohio Supercomputer Center, USA

  MPI+PGAS Hybrid Programming
  MPI has been a widely ported and dominant programming model in parallel computing for the past few decades. As a result, most scientific applications are written using MPI. System advances including large shared memory nodes and low latency direct memory access between nodes provided on modern networks provide support for a wider range of programming models. It is widely believed that a hybrid programming model (MPI+X, where X is a PGAS model) is optimal for many scientific computing problems, especially for exascale computing. MVAPICH2-X provides a unified high-performance runtime that supports both MPI plus PGAS programming models on InfiniBand clusters. This talk will provide an overview of PGAS programming model. Introduce the high-performance unified runtime in MVAPICH2-X and review some recent MPI+PGAS application studies from the OSU Network-Based Computing Laboratory.

• André-Marie Tremblay, Université de Sherbrooke, Canada

  Strongly correlated superconductivity in cuprates and layered organics: results and some algorithmic details
  In cuprates, the Mott insulating state is reached by doping. Pressure, or bandwidth control, tunes the Mott transition in layered BEDT organics. Superconductivity can occur in the metallic phases of both types of compounds near the Mott insulator. This "strongly correlated superconductivity" exhibits special features, discussed in this talk, that distinguish it from BCS superconductivity. Comparisons with experiment and a few predictions will be presented. The results are obtained with cellular-dynamical mean-field theory using the continuous-time hybridization-expansion (CT-HYB) impurity solver. I will also explain how considerable speedup of CT-HYB can be obtained using skip-list concepts and how ergodicity can be implemented in the CT-HYB algorithm in the presence of broken symmetry.

• Ilya Vekhter, Louisiana State University, USA

  Quasiparticle Étouffée: unconventional superconductors probed by magnetic field
  In many materials superconductivity arises from the same strong electron-electron interactions that give rise to unconventional metallic properties, and present challenges for computational approaches. Superconducting state in such systems is anisotropic, strongly varying with the direction of motion of the electrons. Determining this anisotropy is a crucial step in identifying the origin of superconductivity and dominant interactions. In this talk I will introduce and review theoretical ideas and experimental methods for studying anisotropic superconductors. I will show how the dependence of the thermal properties on the direction of the applied magnetic field allows determination of the symmetry of the superconducting state. I will use examples from heavy fermion compounds, pnictides, and organic superconductors, and discuss the successes and challenges of this approach.

• Martin Weigel, Coventry University, United Kingdom

  Simulating spin models on GPU: A tour
  Over the last couple of years it has been realized that the vast computational power of graphics processing units (GPUs) could be harvested for purposes other than the video game industry. This power, which at least nominally exceeds that of current CPUs by large factors, results from the relative simplicity of the GPU architectures as compared to CPUs, combined with a large number of parallel processing units on a single chip. To benefit from this setup for general computing purposes, the problems at hand need to be prepared in a way to profit from the inherent parallelism and hierarchical structure of memory accesses. In this overview lecture I discuss the performance potential for simulating spin models, such as the Ising or Heisenberg models as well as the Edwards-Anderson spin glass, on GPU as compared to conventional simulations on CPU. Different algorithms, including Metropolis and cluster updates, as well as computational tricks such as multi-spin coding are taken into account. A very recent development concerns simulations using population annealing, a new generalized ensemble heuristic that is particularly well suited for massively parallel architectures.

Workshop: Sunday February 15 and Monday February 16, 2015

• Alex Brandt, Rackspace, USA, Physics B.S.

  How I learned to stop worrying and live in business
  Physics B.S. - A degree that is used by many for any purpose the wielder chooses. This is the personal journey of one student's arrival in business after acquiring a degree in Physics. Alex's journey will explore what a Physics degree provides and how all Physics graduates use their degree daily. Alex is a Cloud Evangelist at Rackspace. Today he develops support and technology solutions to better Rackspace. Previously his work focused on training employees in Cloud, Python, Ruby, and Chef. He regularly consults with Rackspace customers to develop unique solutions while internally developing new approaches with evolving technologies. Alex holds a degree in Computer Science and Physics from Minnesota State University, Moorhead.

• Herbert Fotso, Ames National Lab, USA

  Field-driven quantum systems, From transient to steady state
  Nonequilibrium dynamical mean field theory and nonequilibrium self-consistent strong coupling expansion are used to study the relaxation of correlated quantum systems driven out of equilibrium by DC electric fields. Both the Falicov-Kimball and the Hubbard model are found to exhibit different relaxation scenarios suggesting that driven quantum systems have a richer behavior than their quenched counterparts and that integrability does not play as critical a role. In the monotonic thermalization scenario, the system evolves through successive quasi-thermal states and it is possible to extrapolate its long time properties from its transient; bridging the gap between the transient and the steady state with very little computational cost. Furthermore, regardless of the relaxation scenario, it is interesting to ask how the particles are distributed as the system evolves in time. We will show that non-trivial parameter-dependent patterns are formed when the system is visualized in momentum space. These features should be observable in current cold atom experiments.

• Sean Hall, Carver Scientific, USA

  Some surprising thoughts and realizations from a would be research scientist about employment in the 'Real World'
  Sean will talk about his experiences looking for employment and working at Carver Scientific, a small energy storage company specializing in capacitors and coatings. Sean holds a B.S. Degree in Computer Science and a M.S. Degree in Physics from Southern University in Baton Rouge. He has been recently awarded of a patent for a novel energy storage device.

• Kalani Hettiarachchilage, Louisiana State University, USA

  Ferromagnetism in a two-dimensional two species bosonic Hubbard model
  We study a doped two-dimensional bosonic Hubbard model with two hard-core species with different masses using quantum Monte Carlo simulations. With doping we find several distinct phases, including a novel phase separated ferromagnet with Mott insulating behavior for the heavy species and both Mott insulating and superfluid behaviors for the light species. Introducing an imbalance in the population between species, we find a fully phase-separated ferromagnet. By using finite size scaling of the susceptibility, we find the critical exponent of the transition related to the two-dimensional Ising universality class. Since the global entropy of this phase is higher than that of the other magnetic phases and the effects of trapping potential in the different phases is crucial in identifying them experimentally, we investigate the existing of the ferromagnetic phase in the presence of a harmonic trapping potential. It is emphasized that such trapping effects can lead to have the ferromagnetic phase in both hard-core and soft-core bosons. This may provide a new avenue to realize magnetic phases in cold atom experiments. Work in collaboration with V. G. Rousseau, K.M. Tam, J. Moreno, and M. Jarrell (Louisiana State University).

• Václav Janiš, Acad. Sciences, Czech Republic & Louisiana State University, USA

  Ergodicity in statistical mechanics of interacting and disordered systems: Destroying and restoring equilibrium ergodic states
  Ergodicity in statistical mechanics of interacting and disordered systems: Destroying and restoring equilibrium ergodic states.} Statistical mechanics was introduced as a microscopic description of macroscopic thermodynamic phenomena. Laws of statistical mechanics become relevant for the thermodynamics only for infinite volumes, called thermodynamic limit. Such a limit exists only under certain assumptions, the most important of which is ergodicity. We discuss the irreplaceable role of ergodicity in the statistical description of thermodynamic equilibrium. There are, however, equilibrium situations when ergodicity is broken. Typically, ergodicity is broken at phase transitions with a broken symmetry of the Hamiltonian. Phase transition in frustrated disordered systems cause, however, ergodicity breaking without any apparent broken symmetry of the Hamiltonian. We discuss the way the ergodicity breaking is treated in lattice spin models. We introduce the concept of symmetry-breaking fields to restore ergodicity at symmetry-breaking phase transitions. Further on we introduce replicas and hierarchical replications of the phase space of spin variables to successively restore an ergodic state in the mean-field theory of spin glasses with phase transitions without any symmetry breaking. We exemplify restoration of ergodicity in the low-temperature phases of the Ising spin model for a ferromagnet and a spin glass.

• Erik Koch, German Research School for Simulation Sciences, Jülich, Germany

  The Lanczos Method
  See lecture notes at http://www.cond-mat.de/events/correl11/manuscripts/koch.pdf

• Wei Ku, Brookhaven National Lab, USA

  How to construct symmetry-respecting Wannier functions

• Peter Reis, PosiTech Corp., USA

  Using Physics and Computation in Industry
  Peter will talk about how he uses Physics to design electric and hydraulic circuits in Industrial Automation and how he uses Computation to program modern electrical circuits using the Programmable Logic Controller (PLC). In particular he will briefly describe how he configure the PLC using ladder logic.

• Rudolf Roemer, University of Warwick, United Kingdom

  Sparse matrix diagonalization, what it is, why and when it works.

• Valy G. Rousseau, Louisiana State University, USA

  The superfluid density in systems with complex interactions
  In the last decade, the development and the improvement of quantum Monte Carlo algorithms combined with the increased power of computers has opened the way to the exact simulation of Hamiltonians that include various types of interactions, such as inter-species conversion terms or ring-exchange terms. Simultaneously, developments made in the field of optical lattices, laser cooling and magneto/optical trapping techniques have led to ideal realizations of such Hamiltonians. A wide variety of phases can be present, including Mott insulators and superfluids, as well as more exotic phases such as Haldane insulators, supersolids, counter-superfluids, or the recently proposed Feshbach insulator. These phases are characterized by a set of order parameters, one of which being the superfluid density. It is well known that the superfluid density can be related to the response of the free energy to a boundary phase twist, or to the fluctuations of the winding number. However, these relationships break down when complex interactions are involved. To address this problem, I will propose a general expression of the superfluid density, derived from real and thought experiments.

• Shi-Quan Su, University of Tennessee, Knoxville, USA

  A Distributive Linear Algebra Approach for Scalable Computing Platform with Accelerator
  The heterogeneous architecture on su- percomputers evolves in a fast pace, many of the top-ranked supercomputers take advantage of accelerators, such as the Intel Xeon Phi Many Integrate Core (MIC) or NVIDIA Graphics Processing Unit (GPU). But the software development lags behind in attaining high performance when dealing with heterogeneity. The large-scale dense matrix computation is a backbone of modern numerical simulations, such as thermal analysis, analysis using the boundary element method, and electromagnetic wave calculations in fusion application. Here we offer a solution, a high throughput parallel linear algebra package adapted to supercomputing platform with accelerator. On the front end, the users see the same library of functions as ScaLAPACK which they use everyday, plus they have the performance close to the theoretical peak of the accelerator device. Behind the scene, the algorithm is redesigned to conceptually embed the consideration of heterogeneity in every step, and implement with the latest architecture features. Work in collaboration with Eduardo D'Azevedo, Ki Sing Chan, and Kwai Wong (Oak Ridge National Lab.).

• Shuxiang Yang, Louisiana State University, USA

  Numerical study of the periodic Anderson model with a quarter-filled conduction band
  Using the dynamical cluster approximation with continuous-time quantum Monte Carlo as the cluster solver and the recently introduced dual-fermion method, we study the underlying physics of the periodic Anderson model where the conduction band is near quarter-filling while the f-band electron band is half filled. For these parameters, the RKKY coupling changes its nature from ferromagnetic to anti-ferromagnetic, yielding an interesting phase-diagram. Especially, we find the charge ordering of the conduction band is strongly enhanced, which could be due to the proximity to a quantum critical point. Work in collaboration with Juana Moreno and Mark Jarrell (Louisiana State University).

• Peng Zhang, Carnegie Institution of Washington, USA

  DFT+DMFT study of magnetic properties in FeO at high pressure
  FeO is an insulator with anti-ferromagnetic (AFM) spin ordering at ambient pressure. As the external pressure is increased, the Néel temperature first increases when the pressure is below 20 GPa. It has been experimentally predicted that above 80 GPa the AFM ordering will collapse. The mechanism leading to such high pressure magnetic collapse is still under debate. We use the density functional theory plus dynamical mean-field theory (DFT+DMFT) to detect the nature of magnetic collapse in FeO at high pressure. Work in collaboration with R. E. Cohen (Carnegie Institution of Washington & University College London) and K. Haule (Rutgers University).

• Yi Zhang, Louisiana State University, USA

  Study of multiband disordered systems using the typical medium dynamical cluster approximation
  We generalize the typical medium dynamical cluster approximation to disordered systems with multiple bands. Using our extended formalism, we perform a systematic study of the non-local correlation effects induced by disorder on the density of states and the mobility edge of the Anderson localized states. We apply our method to the three dimensional multiband Anderson model with both inter- and intra-band hopping and disorder potential and find fast convergence with increasing cluster size. Our results are consistent with the ones obtained by the transfer matrix and the kernel polynomial methods. Our findings show that the typical medium dynamical cluster approximation method can be used to study the Anderson localization in real materials.