Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session G43: Precision Many-Body Physics IV: Novel Methods and AlgorithmsFocus
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Sponsoring Units: DCOMP DAMOP DCMP Chair: Evgeny Kozik, Kings Coll Room: 702 |
Tuesday, March 3, 2020 11:15AM - 11:51AM |
G43.00001: The variational and diagrammatic quantum Monte Carlo approach to the many-electron problem Invited Speaker: Kun Chen Two of the most influential ideas developed by Richard Feynman are the Feynman diagram technique and his variational approach. Here we show that combining both, and introducing a diagrammatic quantum Monte Carlo method, results in a powerful and accurate solver to the generic solid state problem, in which a macroscopic number of electrons interact by the long-range Coulomb repulsion. We apply it to the quintessential problem of solid state, the uniform electron gas, which is at the heart of the density functional theory success in describing real materials, yet it has not been adequately solved for over 90 years. Our method allows us to calculate numerically exact momentum and frequency resolved spin and charge response functions. This method can be applied to a number of moderately interacting electron systems, including models of realistic metallic and semiconducting solids. |
Tuesday, March 3, 2020 11:51AM - 12:27PM |
G43.00002: Modern diagrammatic many body techniques. Invited Speaker: Riccardo Rossi In this talk I will discuss recent progress on the development of unbiased diagrammatic techniques for strongly-correlated many-body systems. The formalism we have developed allows to elegantly and efficiently encode the fundamental structure of quantum-many theory using renormalized expansions as the building block. Within this framework it is easy to incorporate, for instance, well-established many-body approximations like Dynamical Mean Field Theory as the starting point of a pertubative expansion. In particular, I will present state-of-the-art results in two and three dimensional Fermi-Hubbard models away from half filling in the non-perturbative regime. |
Tuesday, March 3, 2020 12:27PM - 12:39PM |
G43.00003: Faster-than-the-Clock Quantum Monte Carlo Fedor Simkovic, Michel Ferrero, Riccardo Rossi In this talk we present a way to naturally merge and extend Monte Carlo accelation techniques with the sampling of set functions, which can be viewed as the partition function of a bosonic system. The algorithm is particularly suited for the Connected Determinant Diagrammatic Monte Carlo algorithm (CDet) as well as its extensions and generalizations. Our proposed algorithm is rejection-free and allows for variance and autocorrelation time reduction by making use of the exponential information contained in the full set structure. Finally, we present numerical results for the two-dimensional Hubbard model obtained with this technique. |
Tuesday, March 3, 2020 12:39PM - 12:51PM |
G43.00004: A light weight regularization for wave function parameter gradients in quantum Monte Carlo Shivesh Pathak, Lucas Wagner The parameter derivative of the expectation value of the energy is a key ingredient in variational quantum Monte Carlo (VMC) wave function optimization methods. A naive Monte Carlo estimate of this derivative suffers from an infinite variance which inhibits the efficiency of optimization methods which rely on a stable estimate of the derivative. In this work we derive a simple regularization of the naive estimator which is easy to implement and has a neglible bias. This regularization is trivial to implement in a standard VMC code without sampling complex distributions and it can be extrapolated to zero bias without extra computation. |
Tuesday, March 3, 2020 12:51PM - 1:03PM |
G43.00005: Measuring Rényi Entanglement Entropies in Lattice Worm Algorithm Quantum Monte Carlo Emanuel Casiano-Diaz, Chris M Herdman, Adrian Del Maestro In this talk we report on an extension of lattice worm algorithm quantum Monte Carlo that allows for the exact simulation of interacting bosons at zero temperature. We will discuss the implementation of the SWAP technique within the lattice path integral framework that provides access to novel estimators, including the Rényi entanglement entropies without complete knowledge of the density matrix. This technology can be used to probe the scaling of entanglement between spatial subregions and may be useful in understanding the quantum information encoded in ultracold lattice gases that can be probed via a quantum gas microscope. |
Tuesday, March 3, 2020 1:03PM - 1:15PM |
G43.00006: Diagrammatic Monte Carlo for Molecules Jia Li, Markus Wallerberger, Emanuel Gull Electron correlations in chemical systems give rise to a wide range of interesting physical properties. Although traditional mean-field quantum chemical algorithms can reliably calculate ground state observables in many cases, finite temperature and spectral properties are only accessible with explicit inclusion of electron correlations. Diagrammatic Monte Carlo (DiagMC), which expands the physical observable in terms of connected Feynman diagrams and samples the resulting series stochastically, is a powerful technique for studying electron correlations and does not suffer from numerical sign problem which worsens with increasing system size. Recent developments in DiagMC algorithms have greatly improved their numerical efficiency. In this talk, I aim to introduce our DiagMC implementation for multi-orbital systems, and present our results when it is applied to realistic molecular systems. |
Tuesday, March 3, 2020 1:15PM - 1:27PM |
G43.00007: Hybridizing Pseudo-Hamiltonians and Non-local Pseudopotentials in Diffusion Monte Carlo Jaron Krogel, Fernando Reboredo Projector quantum Monte Carlo (QMC) methods are among the most accurate many body techniques to query the properties of the electronic ground state. Due to computational efficiency, non-local pseudopotentials (NLPPs) are used in QMC is for all but light elements. This comes at the price of localization approximations (LAs) that can degrade total accuracy. An alternate pseudo-Hamiltonian (PH) approach that does not require LA was considered early in the QMC history of core pseudization [PRL 62 2088 (1989)], but was not adopted as producing adequate potentials was difficult. In this work, we explore the hybridization of NLPPs and PHs in an attempt to reduce the non-local components. For 3d transition metals we show that hybrid PHs can be as accurate as NLPPs, but with a much smaller non-local part. We find that a simple approach to partitioning scattering channels between the NLPP and PH compoents does not lead to a reduction of localization error, but instead aligns the behavior of the prevailing locality and T-moves approximations. Reasons for this behavior and possible avenues for direct minimization of localization error are discussed. |
Tuesday, March 3, 2020 1:27PM - 1:39PM |
G43.00008: Excitations with Diffusion Monte Carlo: a bottom-up approach. Fernando Reboredo The applications of diffusion Monte Carlo (DMC) have been largely focused on properties of the ground state. As a result, high quality methods to obtain and optimize the ground-state trial wavefunctions are available. However, since much of the phenomena in Solid State Physics is governed by low energy excitations, attempts to extend DMC for the calculations of excited states properties are also documented in the literature. Most of those attempts focus on the direct calculation of excitations. In this talk we will discuss an alternative approach: how to extract excited state properties as an observable of the many-body ground state evaluated within a standard DMC method. The theory will be tested in a model system and compared with exact solutions. The potential limitations of this indirect approach for large systems of interest for real material problems will be discussed. |
Tuesday, March 3, 2020 1:39PM - 1:51PM |
G43.00009: Diagrammatic Monte Carlo for real materials Sam Azadi, Arkadiy Davydov, Evgeny Kozik We present a systematic method for reaching beyond the GW approximation by Diagrammatic Monte Carlo (DiagMC) for first-principle simulations of real materials. DiagMC is used to provide an efficient estimation of higher-order self-energy and polarisability diagrams to achieve a controlled solution for ab initio Hamiltonians. |
Tuesday, March 3, 2020 1:51PM - 2:03PM |
G43.00010: Evaluation of arbitrary Feynman graphs via algorithmic methods. James P. F. LeBlanc Feynman diagrammatics is a powerful tool for the study of correlated electron systems. However, the formulation of diagrams in terms of Matsubara frequencies is not well suited to numerical computations due to an intrinsic inability to evaluate the unbounded Matsubara frequency integrals. In this talk we present an algorithm for fully symbolic evaluation of arbitrary Feynman diagrams that overcomes this issue, and many others. Further, from this perspective of analytics we identify a procedure for high order diagrams which allows for the optimal reduction of the sign problem. This is accomplished via invariant transformations that allow us to group diagrams whose integrands are analytically equal or analytically cancel. |
Tuesday, March 3, 2020 2:03PM - 2:15PM |
G43.00011: Diagrammatic Monte Carlo for attractively interacting fermions Gabriele Spada, Riccardo Rossi, Takahiro Ohgoe, Fedor Simkovic, Michel Ferrero, Kris Van Houcke, Félix Werner A major long-standing goal is the precise computation of properties of interacting many-fermion systems. By evaluating connected Feynman diagrams, the diagrammatic Monte Carlo approach works directly for infinite system size. Thanks to efficient Monte Carlo algorithms, one can reach high enough orders to observe convergence up to a small error bar, provided the diagrammatic series is sufficiently well behaved, if necessary after applying a divergent-series resummation procedure. A crucial ingredient is to use dressed propagators or vertices as building blocks of the diagrams, and to expand around an appropriate starting point. The functional integral formalism allows to justify the validity of such reorganized expansions and their resummability, even for a zero convergence radius. I will present results for two cases of experimental relevance: The normal phase of the unitary Fermi gas, and the superfluid phase of the attractive Hubbard model. |
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