Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session L22: Theory and Simulations of Strongly Correlated Systems with DisorderFocus

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Sponsoring Units: DCOMP Chair: Richard Scalettar, University of California, Davis Room: 321 
Wednesday, March 16, 2016 11:15AM  11:51AM 
L22.00001: Magnetic moments and nonFermiliquid behavior in quasicrystals Invited Speaker: Eric Andrade Motivated by the intrinsic nonFermiliquid behavior observed in the heavyfermion quasicrystal Au51Al34Yb15, we study the lowtemperature behavior of dilute magnetic impurities placed in metallic quasicrystals. We find that a large fraction of the magnetic moments are not quenched down to very low temperatures, leading to a powerlaw distribution of Kondo temperatures, accompanied by a nonFermiliquid behavior, in a remarkable similarity to the Kondodisorder scenario found in disordered heavyfermion metals. [Preview Abstract] 
Wednesday, March 16, 2016 11:51AM  12:03PM 
L22.00002: The Knight shift anomaly in the disordered periodic Anderson model Raimundo dos Santos, Natanael Costa, Thereza Paiva, Nicholas Curro, Richard Scalettar In some materials, the coherence temperature $T^*$ signals the regime in which one has a heavyelectron fluid and `dissolved' local moments. An experimental signature of $T^*$ is provided by the Knight shift anomaly in NMR measurements. Further, the contribution of the heavyelectron fluid to the Knigh shift, $K_{\mathrm{HF}}$, displays universal character over a wide range of temperatures. An important probe of the physical mechanisms at play is the random substitution of say, La for Ce in CeRhIn$_5$: this amounts to removing local moments at random sites, and one may wonder whether these universal features are sensitive to the presence of disorder. The Periodic Anderson Model (PAM) captures many aspects of heavyfermion materials, so here we consider the twodimensional PAM with a fraction $x$ of the $f$sites removed at random. Through Determinant Quantum Monte Carlo simulations we find that universality of $K_{\mathrm{HF}}$ persists even in the presence of disorder, which, in turn, allows us to establish that $T^*$ decreases monotonically with $x$, in agreement with available experimental data. Our simulations also shed light into the low temperature behavior of the disordered PAM at low temperatures: the spin liquid phase of the local moments is suppressed upon dilution. [Preview Abstract] 
Wednesday, March 16, 2016 12:03PM  12:15PM 
L22.00003: Strong correlations generically protect dwave superconductivity against disorder Shao Tang, V. Dobrosavljevi\'c, E. Miranda We address the question of why strongly correlated dwave superconductors, such as the cuprates, prove to be surprisingly robust against the introduction of nonmagnetic impurities. We show that, very generally, both the pairbreaking and the normal state transport scattering rates are significantly suppressed by strong correlations effects arising in the proximity to a Mott insulating state. We also show that the correlationrenormalized scattering amplitude is generically enhanced in the forward direction, an effect which was previously often ascribed to the specific scattering by charged impurities outside the copperoxide planes. [Preview Abstract] 
Wednesday, March 16, 2016 12:15PM  12:27PM 
L22.00004: Study of the Anderson localization in real materials using typical medium dynamical cluster approximation Yi Zhang, Ryky Nelson, Hanna Terletska, Conrad Moore, Chinedu Ekuma, KaMing Tam, Tom Berlijn, Wei Ku, Juana Moreno, Mark Jarrell We generalize the typical medium dynamical cluster approximation to multiorbital disordered systems. Combining it with the first principals downfolding and unfolding methods to derive an effective low energy model, we apply our extended formalism to real materials where strong disorder exists. These include, e.g., the iron selenide superconductors K$_x$Fe$_{2y}$Se$_2$ with Fe vacancies, Ga$_{1x}$Mn$_x$N and S doped Si. By looking at the typical density of states, we study the mobility edge and the localization effects in these materials, which is useful to understand the mechanism of their insulating behavior. We find for example, that even the disorder associated with 12\% vacancies in K$_x$Fe$_{2y}$Se$_2$ together with the anisotropy is not sufficient to cause localization. [Preview Abstract] 
Wednesday, March 16, 2016 12:27PM  12:39PM 
L22.00005: Rounding of the firstorder phase transition in the fourcolor AshkinTeller model Ahmed Ibrahim, Thomas Vojta The twodimensional fourcolor AshkinTeller model is investigated by Monte Carlo simulations to analyze the effects of quenched disorder on the firstorder phase transition. We show that the quenched disorder destroys the firstorder phase transition and turns into a continuous one. We study the emerging critical behavior of the disordered AshkinTeller model by using a finitesizescaling analysis and confirm it to be in the clean twodimensional Ising universality class with universal logarithmic corrections. This concurs with perturbative renormalizationgroup predictions by Cardy. We discuss the universality of the arising critical behavior and we compare with earlier results in the literature. [Preview Abstract] 
Wednesday, March 16, 2016 12:39PM  12:51PM 
L22.00006: Charge density waves in disordered media circumventing the ImryMa argument Norm Tubman, Hitesh Changlani, Taylor Hughes Two powerful theoretical predictions, Anderson localization and the ImryMa argument, impose significant restrictions on which phases of matter can exist in the presence of even the smallest amount of disorder in onedimensional systems. These predictions forbid conducting states and ordered states respectively. It was thus of great interest to find out that Anderson localization can indeed be circumvented in one dimensional systems in the presence of correlated disorder. In a similar manner, but for a different physical phenomenon, we show that the ImryMa argument can be circumvented resulting in the formation of stable ordered states in disordered one dimensional systems. We explicitly simulate a family of Hamiltonians of spinless fermions with correlated disorder, where we find that a charge density wave is stable up to a finite critical disorder strength. Having circumvented the ImryMa mechanism, we then investigate other mechanisms in which disordered systems can destroy an ordered state. [Preview Abstract] 
Wednesday, March 16, 2016 12:51PM  1:03PM 
L22.00007: Entanglement Holographic Mapping of ManyBody Localized System by Spectrum Bifurcation Renormalization Group YiZhuang You, XiaoLiang Qi, Cenke Xu We introduce the spectrum bifurcation renormalization group (SBRG) as a generalization of the realspace renormalization group for the manybody localized (MBL) system without truncating the Hilbert space. Starting from a disordered manybody Hamiltonian in the full MBL phase, the SBRG flows to the MBL fixedpoint Hamiltonian, and generates the local conserved quantities and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the MBL phase. In particular, we focus on the $1d$ interacting Majorana chain with strong disorder, and map out its phase diagram using the entanglement entropy. The SBRG flow also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space decorated with small blackholes. [Preview Abstract] 
Wednesday, March 16, 2016 1:03PM  1:15PM 
L22.00008: Disordered XYZ Spin Chain Simulations using the Spectrum Bifurcation Renormalization Group Kevin Slagle, YiZhuang You, Cenke Xu We study the disordered XYZ spin chain using the recently developed Spectrum Bifurcation Renormalization Group (SBRG) numerical method. With large disorder, the phase diagram of the eigenstates consists of three many body localized (MBL) spin glass phases separated by marginal MBL critical phases. We examine the critical phases of this model by probing the entanglement entropy and EdwardsAnderson spin glass order parameter. We also show how longrange mutual information can be used to distinguish these phases (Jian, Kim, Qi 2015). [Preview Abstract] 
Wednesday, March 16, 2016 1:15PM  1:27PM 
L22.00009: Manybody Localization Transition in RokhsarKivelsontype wave functions Xiao Chen, Xiongjie Yu, Gil Young Cho, Bryan Clark, Eduardo Fradkin We construct a family of manybody wave functions to study the manybody localization phase transition. The wave functions have a RokhsarKivelson form, in which the weight for the configurations are chosen from the Gibbs weights of a classical spin glass model, known as the Random Energy Model, multiplied by a random sign structure to represent a highly excited state. These wave functions show a phase transition into an MBL phase. In addition, we see three regimes of entanglement scaling with subsystem size: scaling with entanglement corresponding to an infinite temperature thermal phase, constant scaling, and a subextensive scaling between these limits. Near the phase transition point, the fluctuations of the Renyi entropies are nonGaussian. We find that Renyi entropies with different Renyi index transition into the MBL phase at different points and have different scaling behavior, suggesting a multifractal behavior. [Preview Abstract] 
Wednesday, March 16, 2016 1:27PM  1:39PM 
L22.00010: Computational Analysis of manybody localized phases beyond 1D Benjamin Villalonga Correa, David Pekker, Bryan Clark Anderson localization can persist in the presence of finite interactions, giving rise to what is known as a manybody localized (MBL) phase. The need to access interior eigenstates makes their computational analysis hard for large system sizes. Recently, an MPS ansatz has been successfully applied to the study of long 1D chains in the MBL phase; however, higher dimensional systems remain largely inaccessible to computational methods. We explore a variational approach to overcome this limitation and report on twodimensional MBL phases. [Preview Abstract] 
Wednesday, March 16, 2016 1:39PM  1:51PM 
L22.00011: A tensor network approach to manybody localization Xiongjie Yu, David Pekker, Bryan Clark Understanding the manybody localized phase requires access to eigenstates in the middle of the manybody spectrum. While exactdiagonalization is able to access these eigenstates, it is restricted to systems sizes of about 22 spins. To overcome this limitation, we develop tensor network algorithms which increase the accessible system size by an order of magnitude. We describe both our new algorithms as well as the additional physics about MBL we can extract from them. For example, we demonstrate the power of these methods by verifying the breakdown of the Eigenstate Thermalization Hypothesis (ETH) in the manybody localized phase of the random field Heisenberg model, and show the saturation of entanglement in the MBL phase and generate eigenstates that differ by local excitations. [Preview Abstract] 

L22.00012: ABSTRACT WITHDRAWN 
Wednesday, March 16, 2016 2:03PM  2:15PM 
L22.00013: Pseudospin representation of the twosite AndersonHubbard model Rachel Wortis, Malcolm Kennett The state of an Anderson localized system can be described in terms of the occupation of a set of singleparticle wave functions which are localized in space. When interactions are added, singleparticle wave functions are no longer well defined, so what is a useful description of the state of a manybody localized system and what about it is localized? Given that any system with Hilbertspace dimension 2$^N$ may be described by an Isingtype Hamiltonian, it has been proposed that in a fully manybody localized system the Ising pseudospins in this representation may be chosen to be local. Actually constructing these spins is nontrivial. While a number of approaches have been proposed, few explicit examples exist and almost all work has been on spin systems. Here we present the Hamiltonian of a twosite Hubbard model with disorder and nearestneighbor interactions written in terms of pseudospins, and we explore the form of these pseudospins and their evolution as a function of hopping amplitude. [Preview Abstract] 
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