### Posters - 20th Mardi Gras Conference

#### Chinedu Ekuma, Louisiana State University, USA

**A Typical Medium Dynamical Cluster Approximation for the Study of Anderson Localization**

We develop a systematic typical medium dynamical cluster approximation (TMDCA) to study localization in disordered electronic systems. The TMDCA utilizes the momentum resolved typical density of states and the non-local hybridization function to characterize the localization transitions. We apply the formalism to the Anderson model of localization in one (1D), two (2D), and three (3D) dimensions. In 1D, we find that the critical disorder strength Wc scales inversely with the linear cluster size with a power law, W_{c}∼(1/L_{c})ν; in 2D, W_{c}decreases logarithmically with L_{c}; whereas in 3D, our method successfully captures the localization phenomenon both in low and large disorder regimes. In 3D as a function of cluster size, our method systematically recovers the re-entrance behavior of the mobility edge, obtains the correct W_{c}, and the associated order parameter critical exponent for the Anderson localization. Once combined with electronic structure calculations and more sophisticated many-body techniques for electron interactions, it will open a new avenue for studying localization phenomenon in real materials as well as the competition between disorder and electron correlations.#### Sheng Feng, Louisiana State University, USA

**Study of the Three Dimensional Edwards-Anderson Spin Glass Model in an External Field**

We study the Edwards-Anderson model on a simple cubic lattice with a finite constant external field using a Monte Carlo simulation code, which employs graphics processing units to dramatically speedup the simulation. The parallel tempering method has been used to alleviate the long equilibration time. Conventional indicators, such as the Binder ratio and correlation length, do not show any signs of a phase transition. We also studied R_{12}, or the ratio of spin glass susceptibilities at finite wave numbers, and show it is quite noisy that a systematic analysis cannot come to clear conclusion. We argue that the typical value should be also studied in additional to conventional linear average value, to provide another perspective for the study of phase transition in spin glasses.#### Herbert Fotso, Ames National Lab, USA

**Visualizing the non-trivial momentum distribution of a field-driven correlated light-heavy Fermi-Fermi mixture**

Time-of-flight images are a common tool in ultracold atomic experiments, employed to determine the quasimomentum distribution of the interacting particles. If one introduces a constant artificial electric field, then the quasimomentum distribution evolves in time as Bloch oscillations are generated in the system and then are damped, showing a complex series of patterns. In different-mass Fermi-Fermi mixtures, these patterns are formed from a frustrated phase separation in momentum space that is driven by Mott physics for large electric fields which stabilize them for long times.-
#### 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). #### Patrick Haase, Universität Göttingen, Germany

**A dual-fermion analysis of the Anderson-Hubbard model**

We apply the recently developed dual-fermion method for disordered interacting systems to the Anderson Hubbard model. This method treats both disorder and interactions on an equal footing, takes into account non-local correlations systematically, and thus represents a significant extension of the single-site mean-field description. We analyze the metal-insulator transition as well as the antiferromagnetic transition of the three-dimensional lattice, by looking at both one- and two-particle quantities, such as the local Green's function and the conductivity. Work in collaboration with Thomas Pruschke (Univ. Göttingen), Shuxiang Yang, Juana Moreno, and Mark Jarrell (Louisiana State University).#### Samuel Kellar, Louisiana State University, USA

**Parquet Equations Implemented using HPX**

The study of correlated electron systems is an area gaining increased interest due to the increase of computational resources that have made solving such problems viable. An example of such a problem is solving the Hubbard Model using the Parquet Equations. As the temperature decreases and the system sizes increases, the solution requires a non-linear increase in system resources. The current olution to such an increase in computational requirements is to move the simulation to a parallel system. This requires storing the vertex functions across many different nodes. Communication across various nodes can inhibit the efficient completion of this algorithm. We use a new runtime system (HPX) which dynamically schedules the distribution of work across all processors. Utilizing the advantages of such a system will help the Parquet Equations to find a solution to the Hubbard Model more quickly. It does this through a combination of latency hiding and efficient distribution of the work across the computational resources. Work in collaboration with Bibek Wagle, Ka-Ming Tam and Shuxiang Yang (Louisiana State University).#### Enzhi Li, Louisiana State University, USA

**Periodic Anderson model with electron phonon interactions and its susceptibilities**

The periodic Anderson model (PAM) is used to study the heavy-fermion behavior of transition metal materials and the nature of Kondo Screening. Recently, PAM with electron-phonon interaction was introduced to explain the volume collapse of Cerium under high pressure. It has been known that PAM with electron-phonon interactions will give rise to two phases, local moment and Kondo singlet. They are separated by a first order phase transition line that terminates at a second order phase transition point. However, the local moment phase is destabilized by the residual entropy problem at low temperature. Here we show that the residual entropy can be eliminated through a phase transition to an ordered state at low temperature.#### Zhou Li, Louisiana State University, USA

**Typical medium dynamical cluster approximation applied to Migdal-Eliashberg theory**

We use the recently developed typical medium dynamical cluster approximation (TMDCA) to study Anderson localization and the superconductor-insulator transition. In our analysis both phonons and disorder are treated on equal footing. For phonons we use the Holstein model Hamiltonian and perform analysis for different types of disorder distributions, i.e. binary or box distribution. It is of interest to see how phonons and disorder compete in fine-tuning of this phase transition by re-normalizing the gap parameter. For weak disorder we find that the size of the gap depends on the phonon frequency. Since for large phonon frequencies the Holstein model maps onto an attractive Hubbard model, we focus on the region where the phonon frequency is small and intermediate for both weak and strong disorders.#### Conrad Moore, Louisiana State University, USA

**GPU Accelerated Hirsch-Fye Quantum Monte Carlo**

In Dynamical Mean Field Theory and its cluster extensions, such as the Dynamic Cluster Algorithm, the bottleneck of the algorithm is solving the self-consistency equations with an impurity solver. The discretization of the imaginary time dimension in the Hirsch-Fye Quantum Monte Carlo algorithm makes it a suitable cluster solver for porting to the Graphics Processing Unit (GPU). This work implements optimizations of the algorithm, such as exploiting large data re-use to take even more advantage of the accelerator architecture. We discuss the application of the code for large scale strongly correlated calculations for electronic systems.#### Ryky Nelson, Louisiana State University, USA

**A Study of Disorder in Diluted Magnetic Semiconductor**

Motivated by experimental studies [A. Richardella et al., Science 327, 665 (2010); M. Dobrowolska et al., Nature Mater. 11, 444449 (2012); N. Samarth, Nature Mater. 11, 360-361 (2012); M. E. Flatté, Nature Phys. 7, 285-286 (2011)] addressing the role of impurity disorder in diluted magnetic semiconductors, we investigate the effects of disorder using a simple tight-binding Hamiltonian with random impurity potential and spin-fermion exchange which is self-consistently solved using the typical medium theory. Adopting the typical density of states (TDoS) as the order parameter, we find that the TDoS vanishes below critical values of impurity potential & exchange parameters, which indicates an Anderson localization transition in the system.-
#### 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. #### Elisha Siddiqui, Louisiana State University, USA

**Typical Medium Dynamical Cluster Approximation For Disordered Superconductors**

We study the effect of disorder on a three-dimensional attractive Hubbard model using the typical medium dynamical cluster approximation with the Bogoliubov-de Gennes approach as a cluster solver. We explore the effects of disorder (W) for a fixed interaction strength (U) on the diagonal and off-diagonal typical density of states. As the disorder strength is increased, the pairing parameter (φ) or the off-diagonal typical density of states decreases and vanishes at a critical disorder strength W_{c}while the spectral gap remains finite. This indicates the transition from a superconducting to a super-resistive phase. A further increase in the disorder strength causes the diagonal density of states to vanish at a critical W'_{c}. This shows the transition from a super-resistive to the Anderson insulator phase. Work in collaboration with H. Terletska (Ames National Lab), N. S. Vidhyadhiraja (Nehru Center, Bangalore), C. E. Ekuma, J. Moreno, and M. Jarrell (Louisiana State University).#### Shi-Quan Su, University of Tennessee, Knoxville, USA

**Non-traditional HPC Approach Simulating Acute Kidney Injury (AKI) Recovery Process on XSEDE Platform: Time-Dependent Cellular Automaton (TDCA) Simulation Using Workflow Engine**

Acute Kidney Injury (AKI) is a common and serious injury. Renal tubule epithelial cell (RTEC) injury is the main mechanism of AKI. It is possible that the cellular death which occurs with an RTECs injury can be regulated. The recovery process can be simulated on a high performance computer (HPC). The numerical model is the "Time-Dependent Cellular Automaton" (TDCA). We carry out the simulation in a Non-traditional HPC approach by managing the ensemble runs of the generic serial code on the Workflow engine, Unicore, provided on all the XSEDE platforms. The preliminary numerical result captures the features which qualitatively agree with the process observed in an actual experiment. Work in collaboration with Charles Collins (University of Tennessee).#### Yu-Ting Tam, Sun Yat-Sen University, China & Brookhaven National Lab, USA

**Itinerancy enhanced quantum fluctuation of magnetic moments in iron-based superconductors**

We investigate the influence of itinerant carriers on dynamics and fluctuation of local moments in Fe-based superconductors, via linear spin-wave analysis of a spin-fermion model containing both itinerant and local degrees of freedom. Surprisingly against the common lore, instead of enhancing the (π,0) order, itinerant carriers with well nested Fermi surfaces is found to introduce significant amount of spatial and temporal quantum fluctuation that leads to the observed small ordered moment. Interestingly, the underlying mechanism is shown to be nesting-associated long-range coupling, rather than the previously believed ferromagnetic double-exchange effect. This challenges the validity of ferromagnetically compensated first-neighbor coupling reported from short-range fitting to the experimental dispersion, which turns out to result instead from the ferro-orbital order that is also found instrumental in stabilizing the magnetic order. Work in collaboration with Dao-Xin Yao (Sun Yat-Sen Univ. & Brookhaven National Lab), and Wei Ku (Brookhaven National Lab & Stony Brook Univ.).-
#### 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). #### Ge Yao, Louisiana State University, USA

**Molecular dynamics in finding nonadiabatic coupling for β-NaYF**_{4}: Ce^{3+}nanocrystals

Optical and electronic properties of cerium ions doped into solid host matrices are explored by density functional theory (DFT). A spin-polarized (unrestricted) DFT + U approach is applied to β-NaYF_{4}: Ce^{3+}nanocrystals, in which the Hubbard U − J value is determined through experimental fitting to be 8.5 eV for yttrium, and 2.9 eV for cerium. Molecular dynamics simulations indicate that the energies of the localized f-like orbitals of the Ce^{3+}dopant exhibit strong thermal fluctuations compared to that of the p- and d-shaped orbitals due to charge-density localization. Our observation of mixing between the d and f orbitals of Ce^{3+}ion is consistent with experimental results. Combining time-dependent density matrix methodology, ab initio molecular dynamics, and on-the-fly nonadiabatic couplings simulates nonradiative transitions between electronic states at ambient temperature. Transition rates between individual orbitals decrease with their energy difference, which is similar to the format of the energy gap law. These transitions contribute to integrated rates of nonradiative thermalization of different electronic excitations to the lowest excited state through multiple pathways. The integrated rates of thermalisation decrease with energy difference of the initial photoexcitation and the final excitation. Work in collaboration with Qingguo Meng (Laredo Community College), Mary T. Berry, P. Stanley May and Dmitri S. Kilin (University of South Dakota).-
#### 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. -
#### Yi-Fu Zhang, Louisiana State University, USA

**Topological insulators in staggered flux systems**

Topological insulators are generally characterized by the Z_{2}index, which requires time-reversal symmetry. On the other hand, the staggered flux states, known as orbital antiferromagnet or charge flux phases, break both time-reversal and translational symmetry. In this work, we investigate the behavior of topological insulators within staggered flux. Interestingly, gapless edge states consisting of counter-propagating states with opposite spins survive, and in some regions, a phase with two such pairs of edge states emerges. We exam the robustness of these phases in the presence of disorder and also show the topological phase transitions with varying the disorder strength. These systems demonstrate topological properties similar to but different from the well-known Z_{2}topological theory. Work in collaboration with Wei Ku (Brookhaven National Lab), Juana Moreno and Mark Jarrell (Louisiana State University).