Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session U45: Computational Methods for Statistical Mechanics: Advances and Applications IIIFocus
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Sponsoring Units: DCOMP GSNP Chair: Ying Wai Li, Los Alamos National Laboratory Room: 706 |
Thursday, March 5, 2020 2:30PM - 3:06PM |
U45.00001: Clusters and Surfaces in Reactive Atmospheres at Realistic Conditions: Beyond the Static, Monostructure Description Invited Speaker: Luca Ghiringhelli The processes occurring at surfaces play a critical role in the manufacture and performance of advanced materials, e.g., electronic, magnetic, and optical devices, sensors, and catalysts. A prerequisite for analyzing and understanding the electronic properties and the function of surfaces is detailed knowledge of the atomic structure, i.e., the surface composition and geometry under realistic gas-phase conditions. The key quantity for studying the structure and function of surfaces/clusters in reactive atmospheres is the Gibbs free energy, as function of number of particles, pressure, and temperature. Here, I present a set of methods for the sampling of the configurational space of (nano)clusters and surfaces in reactive (e.g., O2, H2) atmosphere, in the canonical and grand-canonical ensembles, aiming at the unbiased determination of the phase diagrams as function of temperature and partial pressure of the reactive gas. A common trait of the analysis of the dfferent systems is the description of ensembles of structures as function of envornmental variables, i.e., the identification of the invariant, permanent features, within the "noise" of continiously transforming ones. |
Thursday, March 5, 2020 3:06PM - 3:18PM |
U45.00002: Langevin dynamics for linear scaling quantum Monte Carlo Kipton Barros, Benjamin Cohen-Stead, George Batrouni, Richard Theodore Scalettar We discuss recent advances in quantum Monte Carlo (QMC) sampling for models of interacting electrons. A shortcoming of traditional determinant QMC is its cubic scaling with system size. The alternative Langevin approach offers, in principle, linear scaling. With some new tricks, the Langevin method can be very competitive with determinant QMC. Applications to the Holstein model of electron-phonon interactions will be presented. |
Thursday, March 5, 2020 3:18PM - 3:30PM |
U45.00003: Assessing the Quality of Approximate Quantum Dynamics in Condensed Phase via Sum Rules Lisandro Hernandez de la Pena In this work, we discuss a general protocol for analyzing the quality of approximate quantum time correlation functions of non-trivial systems in many dimensions. This approach is based on the generalized deconvolution of the Kubo transformed quantum time correlation function onto an ensemble averaged quantum correlation function, at a given value τ in imaginary time (such that 0≤ τ ≤ β), which leads to a series of sum rules linking derivatives of different order in the corresponding pair of convoluted correlation functions. We focus on the case when τ = β/2 for which all deconvolution kernels become real valued functions and their asymptotic behavior at long times exhibit a polynomial divergence. It is then shown that thermally symmetrized static averages, and the static averages of the corresponding time derivatives, are ideally suited to investigate the quality of approximate quantum time correlation functions at successively larger, and up to arbitrarily long, times. This overall strategy is illustrated analytically for a harmonic system, and numerically for a multidimensional double-well potential and a Lennard-Jones fluid representing liquid neon at 30 K. |
Thursday, March 5, 2020 3:30PM - 3:42PM |
U45.00004: Ground State Properties of the Diluted Sherrington-Kirkpatrick Spin Glass Stefan Boettcher In a numerical study of dilute versions of the Sherrington-Kirkpatrick mean-field spin glass at temperature T=0, we approximate the energies of ground states of ensembles at variable dilution with high accuracy using the Extremal Optimization heuristic [1,2]. We find that the scaling properties of such systems possess exponents that are parametrized by the degree of dilution [3,4]. This is a surprising result, as one would not expect that gradual bond-dilution would continuously change the universality class of a statistical model. (There is no evidence of a percolation transition separating a trivially disconnected regime from a percolation regime, as one might expect.) It may open the door to a perturbative study of finite-size corrections in replica symmetry breaking. |
Thursday, March 5, 2020 3:42PM - 3:54PM |
U45.00005: Evidence of Information Limitations in Bottom-Up Coarse-Graining Models Aditi Khot, Stephen Shiring, Brett Savoie Chemically specific coarse-grained (CG) models exhibit simplified configurational phase spaces and hence, can potentially capture processes that occur on time and length scales that are too costly for direct atomistic simulation. However, there are fundamental and practical problems associated with coarse-graining, such as the incomplete understanding of CG errors in comparison with atomistic simulations, the lack of transferability of typical CG models to new chemistries, and the costly bespoke approach to developing new CG models from scratch. In this talk, I will present recent results on an automated methodology to parameterize CG models from quantum chemistry calculations. Using the throughput of this methodology, we have systematically characterized the sources of error in common bottom-up parameterization methods as a function of dimension reduction for over 50 independently trained CG models. We find clear evidence that these models are systematically information limited, rather than representability limited, which suggests further improvement is obtainable without resorting to more complex functional forms. Additional implications of these findings, as well as the conditions under which representability related errors arise will also be discussed. |
Thursday, March 5, 2020 3:54PM - 4:06PM |
U45.00006: Hilbert Entropy for the Simple and Precise Measurement of Complexity of Two or Higher Dimensional Arrays Seok Joon Kwon Measuring complexity of higher dimensional arrays has been an important way of quantifying information. For the measurement of complexity of 1D vectors, there are a variety of methods of calculating entropies such as sample, permutation, or Lempel-Ziv entropy. Unfortunately, for higher dimensional arrays, it is not possible to employ these entropies. This is due mainly to the information loss in the course of dimension reduction. To address this problem, we introduce space-filling curve (SFC)-based approach. Thanks to the fact that SFC allows information loss-free dimension reduction, we successfully measured complexity by calculating sample entropy of higher dimensoinal arrays. We found that developed algorithm precisely measured the complexity of higher dimensional arrays as well as detected the critical points in the cases of various phase transition experiments. We also observed that the developed algorithm (Hilbert entropy) can measure scale-invariance and fractal dimension of higher dimensional arrays. We proved that the Hilbert entropy for higher dimesional arrays exhibits power law dependence for arrays with self-similarity. |
Thursday, March 5, 2020 4:06PM - 4:18PM |
U45.00007: Computation of correlation functions and various statistical quantities of different types of Random Matrix Ensembles Kazi Alam, Swapnil Yadav, Khandker A Muttalib We propose a method to compute correlation functions for biorthogonal random matrix ensembles with arbitrary confining potential, by inverting the associated Hankel moment-matrix. We show that using this method it is possible to calculate eigenvalue density, two-point correlation functions, gap functions and other statistical quantities of interest for a wide class of log-gas models. The method allows one to calculate such statistical quantities numerically without evaluating the relevant polynomials or generating explicit matrices. We reproduce standard results for a variety of well-known ensembles and show some new results for Muttalib-Borodin ensembles for which analytic or numerical results have not yet been obtained. |
Thursday, March 5, 2020 4:18PM - 4:30PM |
U45.00008: A Parameter Free Genetic Algorithm for Estimating the Dynamic Structure Factor at Zero and Finite Temperature Nathan Nichols, Adrian Del Maestro, Timothy Prisk, Garfield T Warren, Paul E Sokol We report on a self adaptive Differential Evolution for Analytic Continuation (DEAC) algorithm that can be used to reconstruct the dynamic structure factor from imaginary time density-density correlations. Our approach to this long-standing problem in quantum many-body physics achieves improved resolution of spectral features over earlier methods based on genetic algorithms. The need for fine-tuning of algorithmic control parameters is reduced by embedding them within the genome to be optimized. Benchmarks are presented for models where the dynamic structure factor is known exactly and we report new results for quantum Monte Carlo simulations of confined superfluid helium at low temperatures. |
Thursday, March 5, 2020 4:30PM - 4:42PM |
U45.00009: Study of strongly correlated materials at finite temperature with density matrix embedding theory Chong Sun, Garnet Chan Density matrix embedding theory (DMET) is a wavefunction-in-wavefuction embedding scheme, aimed at describing the ground state of large strongly correlated systems. In this talk, the finite temperature extension of ground state DMET, i.e., FT-DMET, is introduced. We show its performance in both model systems such as 2D Hubbard model and realistic materials such as the hydrogen chain and transition metal oxides. The thermal averages of physical observables such as energy are calculated. The Néel transition is also studied and the Néel temperature is approximated for both 2D Hubbard model and transition metal oxides. |
Thursday, March 5, 2020 4:42PM - 4:54PM |
U45.00010: Two-dimensional translation-invariant probability distributions: approximations, characterizations and no-go theorems Zizhu Wang, Miguel Navascués We study the properties of the set of marginal distributions of infinite translation-invariant systems in the 2D square lattice. In cases where the local variables can only take a small number d of possible values, we completely solve the marginal or membership problem for nearest-neighbors distributions (d=2,3) and nearest and next-to-nearest neighbors distributions (d=2). All these sets form convex polytopes in probability space. This allows us to devise an algorithm to compute the minimum energy per site of any TI Hamiltonian in these scenarios exactly. We also devise a simple algorithm to approximate the minimum energy per site up to arbitrary accuracy for the cases not covered. For variables of a higher (but finite) dimensionality, we prove two no-go results. The exact computation of the energy per site of arbitrary TI Hamiltonians with only nearest-neighbor interactions is undecidable. In addition, in scenarios with d≧2947, the boundary of the set of nearest-neighbor marginal distributions contains both flat and smoothly curved surfaces and the set itself is not semi-algebraic. This implies, in particular, that it cannot be characterized via semidefinite programming, even if we allow the input of the program to include polynomials of nearest-neighbor probabilities. |
Thursday, March 5, 2020 4:54PM - 5:06PM |
U45.00011: Stars & Bars: A Compact Representation for Bosonic Occupation States Caleb Usadi, Hatem Barghathi, Adrian Del Maestro An efficient representation of bosonic occupation states is a critical tool for the exact diagonalization of bosonic Hamiltonians. The memory demands of the traditional method of representing such systems, as lexicographically ordered arrays of integers, increases rapidly as system size grows, limiting current studies to approximately 16 particles at unit filling. Representing basis vectors using the combinatoric stars and bars method allows each basis state to be stored as a single 64 bit integer. This optimally compact representation will enable the analysis of new properties of larger bosonic Hamiltonians, including accessible entanglement, which may be useful in evaluating many-body phases as potential candidate quantum resource states. |
Thursday, March 5, 2020 5:06PM - 5:18PM |
U45.00012: Telediagnostics of Heterogeneous Plasma properties of combustion products
according to the characteristics of its braking radiation. MYKOLA POTOMKIN, VOLODYMYR MARENKOV An important applied aspect of the statistical theory of electronic properties of heterogeneous plasma (HP) formations for determining the amplitude-frequency intensity of its braking radiation is considered. New physical model for braking radiation of HP formations, based on the statistical approach of quasi-neutral cell for the description of electron-ion processes in the HP formations is proposed. Stochastic motion of charged plasma particles is presented in sequence of stages of anharmonic oscillations in effective electrostatic field of cells perturbed by particle displacements relative to the electrical centers of the cells of quasi-neutrality in HP formations. |
Thursday, March 5, 2020 5:18PM - 5:30PM |
U45.00013: Bosonic entanglement crossover from groundstate scaling to volume laws Qiang Miao, Thomas Barthel The crossover behavior of eigenstate entanglement entropies from an area law or log-area law for low energies and small subsystem sizes to volume laws for high energies and large subsystems can be described by scaling functions. We demonstrate this for two bosonic systems. The harmonic lattice model describes a system of coupled harmonic oscillators and is a lattice regularization for free scalar field theories. For dimensions d ≥ 2, the ground state of this model displays an entanglement area law, even at criticality, because excitation energies vanish only at a single point in momentum space. In contrast, Bose metals feature a finite Bose surface with zero excitation energy. One hence finds log-area laws for the groundstate entanglement. For both models, we sample excited states. The distributions of their entanglement entropies are sharply peaked around subsystem entropies of corresponding thermodynamic ensembles in accordance with the eigenstate thermalization hypothesis. In this way, we determine the scaling functions numerically. Eigenstates for quasi-free bosonic systems are not Gaussian. We resolve this problem by considering appropriate squeezed states instead, for which entanglement entropies can be evaluated efficiently. |
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