Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session H34: Precision Many Body Physics IFocus

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Sponsoring Units: DCOMP DAMOP DCMP Chair: Lubos Mitas, North Carolina State Univ Room: LACC 409A 
Tuesday, March 6, 2018 2:30PM  3:06PM 
H34.00001: Precision manybody theory for the Hubbard model and beyond: the knowns, the known unknowns, and the unknown unknownns Invited Speaker: Andrew Millis This talk will summarize the present status of our knowledge of the equilibrium properties of the two dimensional Hubbard model, including the regimes of magnetism, superconductivity and the pseudogap and the correlation functions relevant for dynamics. Results obtained by different methods will be compared and regimes of relative agreement and of relative uncertainty will be delineated. The relation of the results to data on cold atom systems and copperoxide high transition temperature superconductors will be discussed and open issues will be highlighted. Brief mention of nonequilibrium physics will be made. 
Tuesday, March 6, 2018 3:06PM  3:18PM 
H34.00002: Dynamical Cluster Dual Fermion expansion Sergei Iskakov , Hanna Terletska , Emanuel Gull The dual fermion series is a diagrammatic approach for correlated lattice models that includes nonperturbative local and perturbative nonlocal dynamic correlations. Unfortunately, strong nonlocal fluctuations, such as those present near half filling in the twodimensional Hubbard model, render the local approximation less suitable as a starting point. In this talk we present a cluster dual fermion method based on an expansion around the dynamical cluster approximation. Unlike previous formulations, our method does not employ a coarse graining approximation to the interaction, which we show to be the leading source of error at high temperature, and converges to the exact result independent of the size of the underlying cluster. 
Tuesday, March 6, 2018 3:18PM  3:30PM 
H34.00003: Diagrammatic Monte Carlo Study of Realistic Systems Jia Li , Markus Wallerberger , Emanuel Gull Diagrammatic Monte Carlo (DiagMC), which expands the free energy in terms of Feynman diagram and samples the resulting series stochastically, is a powerful technique in studying correlated manyelectron problems. However, the application of the technique in real material calculations is limited by the prohibitive size of the Coulomb interaction tensor. 
Tuesday, March 6, 2018 3:30PM  3:42PM 
H34.00004: Is there stripe order or dwave superconductivity in the Hubbard model? Sandro Sorella , Kazuhiro Seki , Luca Fausto Tocchio , Alberto Parola , Federico Becca In a recent paper BoXiao Zheng et al. (arXIV:1701.00054) have claimed that, by using several state of the art numerical techniques, at a particular filling δ =1/ 8 and strong coupling U/t=8, the ground state of the Hubbard model displays charge and spin modulations that are typical of the so called stripe order. In this work we reconsider this model by using standard variational techniques based on quantum Monte Carlo[1]. We use a wider class of variational wavefunctions with a very accurate and systematically convergent description of the ground state properties[2,3]. The final aim of this work is to solve the apparent controversy between standard variational techniques based on Jastrow correlated meanfield approximations, apparently favoring the uniform dwave superconducting solution and DMRG, tensornetwork approximations, on the other hand biased for low entanglement entropy ground states. 
Tuesday, March 6, 2018 3:42PM  3:54PM 
H34.00005: Sign Blessing in the Diagrammatic Space of the Jellium Model Zhiyuan Yao , Nikolai Prokof'ev , Boris Svistunov The jellium model is a basic model of fundamental importance. Quantitative knowledge of its thermodynamics, quasiparticle excitations, and dielectric responses is the starting point for properly treating the Coulomb interaction in more realistic systems. However, numerous numerical methods can either offer only partial information or rely on approximations with unknown systematic bias. Monte Carlo sampling of Feynman diagrams to highorder is a generic way to solve this problem but the best strategy for simulating the diagrammatic space of skeleton diagrams remains unknown. Given that signalternating Feynman diagrams for fermions are known to cancel each other, it is crucially important to better understand the precise mechanisms behind this signblessing phenomenon that leads to better series behavior. We explore relative merits of various approaches based on different representations (real space vs momentum space and imaginary time vs Matsubara frequencies), explicit variables symmetrization, and explicit summation over all, or selected subclasses, of diagram topologies. 
Tuesday, March 6, 2018 3:54PM  4:06PM 
H34.00006: Next Generation of Selected Configuration Interaction and Exact Diagonalization Techniques: The Adaptive Sampling Configuration Interaction (ASCI) Method Norm Tubman , Christian Freeman , Birgitta Whaley Selected configuration interaction techniques (SCI) have been shown to produce especially accurate results for treating strongly correlated Hamiltonians, with applications in lattice models, quantum chemistry, embedding techniques, and excited states. We have recently introduced a new SCI technique, the adaptive sampling CI (ASCI) approach, and demonstrated that this algorithm, together with a heat bath extension of it, are among the most efficient algorithms for treatment of strongly correlated systems. In this work, we show how these adapted CI techniques lead to a new level of accuracy and efficiency for selected CI calculations, when tailored to modern computer architectures. These computational advances allow for simulations with the ASCI algorithm (and other SCI methods) that achieve accuracy beyond what is possible with most other simulation techniques. 
Tuesday, March 6, 2018 4:06PM  4:18PM 
H34.00007: Guaranteed Accuracy Formalism for Imaginary Time Calculations Emanuel Gull , Dominika Zgid Finitetemperature Green's function calculations of quantum systems are frequently performed in the Matsubara formalism, with calculation steps alternating between imaginary time steps (e.g. solution of a lattice model) and Matsubara frequencies (e.g. solution of a Dyson equation). In large systems, these transforms and the illconditioned nature of the Matsubara equations often lead to the amplification of small roundoff and cutoff errors. 
Tuesday, March 6, 2018 4:18PM  4:30PM 
H34.00008: Next Generation Dynamical MeanField Theory Calculations: the ASCIDMFT Method Carlos Mejuto Zaera , Norm Tubman , Birgitta Whaley The study of strongly correlated electronic systems is one of the main open challenges in condensed matter physics. The dynamical meanfield theory (DMFT) method, which selfconsistently maps an intractable strongly correlated lattice problem into a numerically solvable impurity Anderson model, has been very successful in describing the quantum phases and spectra of phenomenological and ab initio models. However, the range of physics that can be studied with DMFT is naturally limited by the complexity of impurity models that the algorithm can handle. For zero temperature studies, configuration interaction (CI) methods have been introduced into DMFT calculations to efficiently compute the ground state of the impurity Hamiltonian. Here we employ the recently proposed adaptive sampling CI (ASCI) algorithm, building on its key ability to identify the most relevant states to describe the ground state in a given basis, to solve the impurity model and thereby construct an extremely efficient ASCIDMFT algorithm. We provide evidence that this novel implementation will be able to perform with higher efficiency and better scaling than previous zero temperature DMFT impurity solvers, opening the door to a new generation of studies of strongly correlated physics. 
Tuesday, March 6, 2018 4:30PM  4:42PM 
H34.00009: Unbiased ManyBody calculations with DysonSchwinger equations: A novel approach to functional integrodifferential equations. Tobias Pfeffer , Lode Pollet We show how to derive a suitable closed set of functional integrodifferential equations based on DysonSchwinger equations and introduce the necessary tools to find an unbiased numerical solution. The key concepts are the Homotopy Analysis Method and the adaptation of this semianalytic method from differential equations to the diagrammatic language of field theory. The resulting diagrams can be summed up by a stochastic sampling procedure. Taking all these techniques into account provides a novel approach to solve the infinite hierarchy of DysonSchwinger equations without any truncation. 
Tuesday, March 6, 2018 4:42PM  4:54PM 
H34.00010: When Diagrammatic Monte Carlo Meets BaymKadanoff algorithm: A Systematic Approach for Quantum ManyBody Dynamics Kun Chen , Yuan Huang , Kristjan Haule , Gabriel Kotliar We introduce a bold diagrammatic Monte Carlo approach to study the linear response dynamics of quantum manybody systems. In order to describe the dynamics, it is vital to build the constant of motions into the structure of the Feynman diagrams used to calculate the manybody correlation functions. Using BaymKadanoff algorithm, we fix the conservation law for the two body correlation functions in the G^{2}W skeleton diagrammatic expansion by introducing 3point vertex functions. We then design a diagrammatic Monte Carlo method to selfconsistently calculate high order diagrams for these vertex functions. The obtained twobody correlation functions, which obey all the conservation laws as well as several essential sum rules, give the access to the lowenergy and longwavelength response functions. We demonstrate that our method can be used to study the dynamical structure factor of frustrated Heisenberg model on the triangular lattice with a fermionization technique. 
Tuesday, March 6, 2018 4:54PM  5:06PM 
H34.00011: Determinant Diagrammatic Monte Carlo for the SelfEnergy Fedor Simkovic , Evgeny Kozik Controlled calculations of manyfermion properties by diagrammatic Monte Carlo methods in strongly correlated regimes has been particularly challenging due to the divergence of the bare series and misleading convergence of the skeleton series. With the Hubbard model as an example, we implement a determinant diagrammatic Monte Carlo method for summing irreducible diagrams for the fermionic selfenergy directly in the thermodynamic limit. Our approach allows to compute the selfenergy in the momentum and Matsubara frequency space up to unprecedentedly high diagram orders, which enables the application of a broad range of analytic continuation methods leading to accurate results in strongly correlated regimes. 
Tuesday, March 6, 2018 5:06PM  5:18PM 
H34.00012: Interaction Expansion of the Partition Function with Action Shifts Markus Wallerberger , Jia Li , Emanuel Gull In this work, we systematically explore the inclusion of shift terms in the action of Anderson impurity models and their effect on the interaction expansion continuoustime quantum Monte Carlo method. Such terms can either be used absorb the loworder contributions to the series or (approximately) "bosonify" the system. 
Tuesday, March 6, 2018 5:18PM  5:30PM 
H34.00013: Convergence Properties of Fully Dressed Diagrammatic Series and Pathologies of the LuttingerWard Functional Aaram Kim , Evgeny Kozik We access the entire highorder diagrammatic series in terms of the fully dressed Green’s function G and the fully dressed screened interaction W by means of the Diagrammatic Monte Carlo method, and explore its convergence properties in connection with the recently discovered multivaluedness of the LuttingerWard functional for Hubbardlike models. In particular, we find that the GW series diverges well below the branching point of the LuttingerWard functional, but admits analytic continuation beyond its convergence radius by standard techniques. We further explore the possibility of using fully dressed skeleton diagrammatic series in the strongly correlated regime to obtain precise results with controlled accuracy. 
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