Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session E38: Quantum Many-Body Systems and Methods |
Hide Abstracts |
Sponsoring Units: DCOMP Chair: Lev Vidmar, Pennsylvania State Univ Room: LACC 501A |
Tuesday, March 6, 2018 8:00AM - 8:12AM |
E38.00001: Destruction of Neel Ordering of S=1 Square Lattice Magnets Ribhu Kaul , Julia Wildeboer , Jonathan Demidio We introduce models of spin S=1 that can be simulated sign-problem free with means of a Stochastic Series Expansion Quantum Monte Carlo (SSE QMC). Compared to the S=1/2 case there is a plethora of new phases and phase transitions |
Tuesday, March 6, 2018 8:12AM - 8:24AM |
E38.00002: Directed-Loop Quantum Monte Carlo Method for Retarded Interactions Manuel Weber , Fakher Assaad , Martin Hohenadler The directed-loop quantum Monte Carlo method is generalized to the case of retarded interactions. Using the path integral, fermion-boson or spin-boson models are mapped to actions with retarded interactions by analytically integrating out the bosons. This yields an exact algorithm that combines the highly efficient loop updates available in the stochastic series expansion representation with the advantages of avoiding a direct sampling of the bosons. The application to electron-phonon models reveals that the method overcomes the previously detrimental issues of long autocorrelation times and exponentially decreasing acceptance rates. For example, the resulting dramatic speedup allows us to investigate the Peierls quantum phase transition on chains of up to 1282 sites. We show results for the real-space correlation functions and the specific heat of the spinless Holstein model. |
Tuesday, March 6, 2018 8:24AM - 8:36AM |
E38.00003: Parametrization of the spectrum in stochastic analytic continuation Hui Shao , Anders Sandvik We present progress in the stochastic sampling approach to numerical analytic continuation of imaginary-time dependent correlation functions computed with quantum Monte Carlo simulations. The spectral functions are parametrized as a sum of \delta-functions in the continuum with fixed amplitudes and adjustable locations. This form can be efficiently sampled and is a good starting point for introducing various constraints and additional features. We introduce a simple criterion for choosing the optimal temperature that leads to sampling of only statistically relevant spectral features (avoiding over-fitting). Further more, we demonstrate how various prominent spectral features, e.g., edges and isolated \delta-functions, can be incorporated with the sampling approach and lead to significantly better fidelity. |
Tuesday, March 6, 2018 8:36AM - 8:48AM |
E38.00004: Efficient vertex parametrization for the constrained functional renormalization group for effective low-energy interactions Carsten Honerkamp We present an efficient approximation for the perturbative calculation of electron-electron interaction in multi-orbital lattice systems. By using ideas for channel decomposition, form factor expansion and the truncated unity functional renormalization technique we describe the interaction as arising from the non-local an orbital-dependent coupling of spin-diagonal and spin-changing particle-hole bilinears as well as particle-particle bilinears that each reside within the same orbital. This allows us to employ a rather fine momentum discretization which e.g. gives insights on the non-local screening of spin and charge interactions. Using this formalism we compute the effective low-energy interactions in a three-band model where the two bands away from the Fermi levels are integrated out with the constrained functional renormalization group (cfRG). We show that the cfRG adds important features to the effective model that cannot be found using the constrained random phase approximation (cRPA). |
Tuesday, March 6, 2018 8:48AM - 9:00AM |
E38.00005: Irreversible dynamics in quantum many-body systems Markus Schmitt , Stefan Kehrein Irreversibility, despite being a necessary condition for thermalization, still lacks a sound understanding in the context of quantum many-body systems. In our work [1] we approach this question by studying the behavior of generic many-body systems under imperfect effective time reversal, where the imperfection is introduced as a perturbation of the many-body state at the point of time reversal. Based on numerical simulations of the full quantum dynamics we demonstrate that observable echos occurring in this setting decay exponentially with a rate that is intrinsic to the system meaning that the dynamics is effectively irreversible. |
Tuesday, March 6, 2018 9:00AM - 9:12AM |
E38.00006: Localization and Dynamics in the Strongly Driven Anderson Insulator and Related Models Ravindra Bhatt , Kartiek Agarwal , Sriram Ganeshan We study localization and charge dynamics in a monochromatically driven one-dimensional Anderson insulator [1] as well as related models using a mapping of the Floquet Hamiltonian to a hopping problem with correlated disorder in one higher harmonic-space dimension. We focus on the low-frequency, strong-driving regime in this work. Resonances in the analogous model are shown to correspond to adiabatic Landau-Zener (LZ) transitions between lattice sites. These resonances lead to dynamics that appear diffusive over a single drive cycle, but localize into orbits which can be interpreted as the Floquet eigenstates. Actual charge transport occurs over many drive cycles due to dephasing between Mott-like pairs of these orbits and has a logarithmic time dependence. Further, applying a spatially-varying random phase to the drive tends to decrease localization, suggestive of weak-localization physics. We contrast these findings with results obtained for strong drives in related models with extended states with and without topological protection. |
Tuesday, March 6, 2018 9:12AM - 9:24AM |
E38.00007: Entropy functional approach for Fermionic lattice models Zhengqian Cheng , Chris Marianetti We formulate an entropy functional of a particular subset of reduced density matrix (RDM) for interacting Fermionic lattice models, which includes all local elements of the RDM (ie. all local N-body contributions); while the only nonlocal contributions are confined to the single-particle density matrix. We propose dual symmetric approximations for the unknown entropy functional (i.e. the value and domain) and evaluate it as compared to numerically exact or highly accurate ground state properties (i.e. Hubbard models in 0d, 1d, 2d, d=inf). Our approach is sufficiently precise in both low dimensional and high dimensional systems, as compared to approaches such as density matrix renormalization group and dynamical mean-field theory; which are numerically exact in one limit and inapplicable or unreliable in the other. Furthermore, our approach has a relatively small computational cost and could be highly applicable in the context total energies of strongly correlated materials and molecules. |
Tuesday, March 6, 2018 9:24AM - 9:36AM |
E38.00008: Tensor decomposition method for strongly correlated few-body systems Airi Kawasaki , Osamu Sugino Antisymmetrized geminal power (AGP) theory [1], closely related to BCS theory of superconductors, is a mean-field theory of electron pairs (geminals) and provides a basis for a wave function theory. When a many-body wave function is expanded by AGP, resulting AGP-CI series converges much faster than the configuration interaction (CI) series of Slater determinants, thereby enabling a compact representation of correlated wave functions [2,3]. This AGP-CI theory is extended here for further compact representation of the wave function by removing the orthogonality constraint on geminals. When removing the orthogonality constraint, known formula cannot be used to obtain the Hamiltonian matrix elements making the theory numerically intractable. We overcome this problem by using a mathematical theory of tensor decomposition. In this talk, we present the methodology and discuss application to Hubbard models. |
Tuesday, March 6, 2018 9:36AM - 9:48AM |
E38.00009: Dynamical Mean Field Theory, Density-Matrix Embedding Theory and Rotationally Invariant Slave Bosons: a Unified Perspective Tsung-Han Lee , Thomas Ayral , Gabriel Kotliar We present a unified perspective on Dynamical Mean Field Theory (DMFT), Density-Matrix Embedding Theory (DMET) and Rotationally Invariant Slave Bosons (RISB). We show that DMET can be regarded as a simplification of the RISB method where the quasiparticle weight is set to unity. This relation allows to easily transpose extensions of a given method to another: for instance, a temperature-dependent version of RISB can be used to derive a temperature-dependent free-energy formula for DMET. |
Tuesday, March 6, 2018 9:48AM - 10:00AM |
E38.00010: Cluster expansion and the Feynman path-integral Anish Bhardwaj , Efstratios Manousakis We develop an approach of calculating the many-body path integral based on the idea of linked cluster expansion. We will discuss the diagrammatic rules for calculating the free-energy and the pair distribution function. The calculated pair-distribution function for distinguishable particles interacting with Lennard-Jones potential, in various attempted schemes of approximation and partial resummations of the diagrammatic series, compares very well with the results of path integral Monte Carlo simulation. Our method can be extended to the case of identical particles and in particular to the case of the many-fermion problem where the quantum Monte Carlo method is plagued by the infamous ``sign''-problem. |
Tuesday, March 6, 2018 10:00AM - 10:12AM |
E38.00011: Correlation consistent pseudopotentials for quantum Monte Carlo and other many-body electronic structure methods: 2nd row elements Michael Bennett , Cody Melton , Abdulgani Annaberdyiev , Guangming Wang , Luke Shulenburger , Lubos Mitas We report on construction and benchmarking of a set of pseudopotentials (PPs) for high accuracy electronic structure calculations for 2nd row atoms. Despite including cases often considered "easy", such as Si, this row poses unique difficulties. In fact, there are number of challenges that stem from the customary Ne-core partition due to the small number of valence electrons and large cores. We found especially that ionic bonds (such as oxides) can exhibit significant errors with respect to all-electron CCSD(T) results, in particular, for non-equilibrium conformations. This applies not only to Na and Mg, but to some extent even to Al and Si. For example, all existing PPs underestimate the repulsive side of polar bonds (say, for systems such as MgO) by tenths of eV. We therefore map-out the possibilities for Ne-core PPs and discuss their accuracy limits. Furthermore, we investigate the possibility of improving PPs by a repulsive term that eliminates this deficiency with little additional computational cost. Finally, for cases where none of the above leads to satisfactory accuracies we construct He-core ECPs that reproduce energetics (spectra and molecular binding curves) with typical errors within 0.003 eV. |
Tuesday, March 6, 2018 10:12AM - 10:24AM |
E38.00012: Correlation consistent pseudopotentials for quantum Monte Carlo and other many-body electronic structure calculations: 3d transition elements. Cody Melton , Michael Bennett , Abdulgani Annaberdyiev , Guangming Wang , Luke Shulenburger , Lubos Mitas We report on the construction and testing of pseudopotentials (PPs) for electronic structure calculations for 3d elements. This follows our recent work for the first and second rows. The construction emphasizes use of relativistic correlated calculations for the construction and simplicity of the resulting operators. Thorough testing in equilibrium and non-equilibrium conformations in molecular settings with hydride and oxide molecules is employed as the initial baseline for benchmarking and transferability tests of the constructions. The constructed PPs show small discrepancies for atomic and ionic excited states as well as consistently small discrepancies for molecular binding curves. The resulting potentials are smooth at the origin and of a semilocal form with a few gaussians per nonlocal channel. This allows their use also in plane wave codes with appropriately higher cut-offs. The PPs overall accuracy in explicitly correlated calculations is much higher than using nonrelativistic all-electron framework with explicit inlcusion of core states. |
Tuesday, March 6, 2018 10:24AM - 10:36AM |
E38.00013: Effective models for the low energy behavior of FeSe from first principles quantum Monte Carlo Brian Busemeyer , Lucas Wagner A major question in the study of iron-based superconductors is what appropriate effective model applies to them. Recently[1], it has become possible to use highly accurate fixed-node diffusion Monte Carlo (FN-DMC) calculations to derive effective models for correlated electron systems. Previous work[2] by our group has shown that FN-DMC provides an accurate accounting of several properties of FeSe. We combine FN-DMC calculations with the model-fitting approach in [1] and a matching pursuit approach to quantify the importance of different interaction and hopping parameters to algorithmically select multiple minimal models for the low-energy degrees of freedom of the system using only first principles data. We will discuss these models and what they mean for the description of this system. [1] H. J. Changlani, H. Zheng, and L. K. Wagner, The Journal of Chemical Physics 143, 102814 (2015). [2] B. Busemeyer, M. Dagrada, S. Sorella, M. Casula, L. K. Wagner, Physical Review B 94, 035108 (2016). |
Tuesday, March 6, 2018 10:36AM - 10:48AM |
E38.00014: Frequency-Dependent Functional Renormalization Group for Interacting Fermionic Systems Nahom Yirga , David Campbell We derive an expansion of the functional renormalization group (fRG) equations that treats both the frequency and momentum dependencies of the vertex in a systematic manner by recasting the fRG equations as a series of Bethe-Salperter equations in the particle-particle, particle-hole, and particle-hole exchange channels. The linearity of the equations offers numerous computational advantages and leads to stable solutions at both the one- and two-loop levels. As the expansion is in the coupling between channels, the truncations that are necessary to make the scheme computationally tractable still lead to equations that treat contributions from all channels equally. We consider the sources of error within the truncations, the computational costs associated with them, and how the choice of regulator affects the flow of the fRG. As benchmarks, we apply different trunctions of the fRG equations to the single-impurity Anderson model. We then use the optimal truncation to study the one-dimensional bond-charge Hamiltonian and the two-dimensional extended Hubbard model. We find that in many cases, the fRG converges to a stable vertex and self-energy from which one can extract the various correlation functions and susceptibilities of interest. |
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