Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session C8: Quantum Many-Body Systems 2: Quantum Monte Carlo Methods |
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Sponsoring Units: DCOMP Chair: Thomas Maier, Oak Ridge National Lab Room: 267 |
Monday, March 13, 2017 2:30PM - 2:42PM |
C8.00001: Coupling quantum Monte Carlo and independent-particle calculations: self-consistent constraint for the sign problem based on density or density matrix Mingpu Qin, Hao Shi, Shiwei Zhang The vast majority of quantum Monte Carlo (QMC) calculations in interacting fermion systems require a constraint to control the sign problem. The constraint involves an input trial wave function which restricts the random walks. We introduce a systematically improvable constraint which relies on the fundamental role of the density or one-body density matrix. An independent-particle calculation is coupled to a constrained path auxiliary-field QMC calculation. The independent-particle solution is used as the constraint in QMC, which then produces the input density or density matrix for the next iteration. The constraint is optimized by the self-consistency between the QMC and independent-particle calculations. The approach is demonstrated in the two-dimensional Hubbard model by accurately determining the ground state when collective modes separated by tiny energy scales are present in the magnetic and charge correlations. Spin and charge-density wave orders are shown to exist at 1/8 doping, and their properties are characterized. Our approach also provides an ab initio way to predict effective interaction parameters for independent-particle calculations. [Preview Abstract] |
Monday, March 13, 2017 2:42PM - 2:54PM |
C8.00002: Exploring AFQMC Calculations in Solids and Molecules Edgar Josue Landinez Borda, Miguel Morales Silva The Auxiliary Field Quantum Monte Carlo (AFQMC) [1] method has been outlined as a promising path to compute the electronic structure of strong correlated molecules and solids [2],[3]. We explore its capabilities in a broad range of solids and molecules with different types of chemical structure and bonding. In addition, we study the use of single and non-orthogonal multi-determinant wave functions [4] in the calculation of of the equation of state and atomization energies of the systems studied. Overall, we finding good agreement with experimental results. $\backslash $[1]Shiwei Zhang, Henry Krakauer, Phys. Rev. Lett. 90. 136401 (2003). $\backslash $f0 [2] S. Zhang, "Auxiliary-Field Quantum Monte Carlo for Correlated Electron Systems, Emergent Phenomena in Correlated Matter, Modeling and Simulation Vol. 3 (2013), Edtied by E. Pavarini, E. Koch, and U. Schollwock.$\backslash $f0 [3] Fengjie Ma, Wirawan Purwanto, Shiwei Zhang, and Henry Krakauer Phys. Rev. Lett. 114, 226401 (2015)$\backslash $f0 [4]Symmetry-projected wavefunctions in Quantum Monte Carlo calculations, H. Shi, C. A. Jim\'{e}nez-Hoyos, R. R. Rodr\'{\i}guez-Guzm\'{a}n, G. E. Scuseria, and S. Zhang,Phys. Rev.B 89, 125129 (2014). [Preview Abstract] |
Monday, March 13, 2017 2:54PM - 3:06PM |
C8.00003: Properties of wave functions/phases on nodal hypersurfaces in electronic structure quantum Monte Carlo Lubos Mitas, Cody Melton, M. Chandler Bennett Electronic structure quantum Monte Carlo (QMC) calculations often employ fixed-node/phase approximations to eliminate the well-known fermion sign problem(s). For real eigenstate the node is a zero locus of electron configurations in the position space, i.e., a codimension-1 hypersurface. We show several new properties of fermionic wave functions, in particular, for real eigenstates and for phases of stationary complex eigenstates on their corresponding nodal surfaces, as they apply for each eigenstate in the spectrum. In particular, for local potentials: a) generically, any spatial derivative of the eigenstate is itself an eigenstate on the node with the same eigenvalue; b) trace of the eigenstate gradient is itself an exact fermionic eigenstate on the node with the same eigenvalue. After some rearrangements related properties apply also to the eigenstate phases for inherently complex wave functions. Assuming continuity of eigenstates low-order derivatives almost everywhere, the node accuracy significantly impacts the wave function in general, supporting recent results on origins of fixed-node errors in QMC calculations. We further analyze the implications of these properties for accuracy of quantum Monte Carlo calculations and fixed-node/phase approximations. [Preview Abstract] |
Monday, March 13, 2017 3:06PM - 3:18PM |
C8.00004: Generation of soft pseudopotentials from and for correlated methods. Michael Bennett, Cody Melton, Luke Shulenburger, Lubos Mitas We study several types of soft, semilocal pseudopotential constructions based on one-body and many-body approaches. The construction is formulated as an (inverse) optimization that can explore several types of optimization criteria, for example, matching one-particle properties such as orbital norm-conservation/shape-consistency, reproducing excitation energies in Hartree-Fock and correlated methods and matching correlated density matrices. It is known that, in general, this is an ill-conditioned problem where additional constraints need to be supplied to achieve converged results in a reasonably robust manner. The constructed effective operators are tested in high accuracy correlated calculations of atoms and small molecules. By a combination of methods we are able to obtain pseudopotentials for selected elements in the first two rows with accuracy that reproduce all-electron excitations and binding curves with ~$0.05$-$0.01$ eV accuracy despite using only a very restricted number of gaussian terms in each L-channel. We therefore show that significant improvements in accuracy of pseudopotentials are feasible and therefore provide an opportunity for an overall increase in the accuracy and efficiency of QMC methods and other correlated approaches for valence-only calculations. [Preview Abstract] |
Monday, March 13, 2017 3:18PM - 3:30PM |
C8.00005: A diagrammatic Monte Carlo root finding approach: The Homotopy Analysis Method applied to Dyson-Schwinger Equations Tobias Pfeffer, Lode Pollet Diagrammatic Monte Carlo is a promising tool to study quantum many-body models. This is because it does not suffer from the exponential scaling of the sign problem with the system's volume as it is the case in path integral Quantum Monte Carlo approaches. It is nevertheless not without its own challenges, notably the series convergence or the inherent difficulties in sampling and storing multi-dimensional objects like 4-point vertices in the skeleton approach. In this talk, we present the construction of a different series of diagrams for the diagrammatic Monte Carlo sampling in non-perturbative parameter regimes. The construction is based on the expansion of a root finding algorithm applied to the Dyson-Schwinger equations in terms of rooted tree diagrams. This method can tackle generic high-dimensional integral equations, avoids the curse of dealing with high-dimensional objects, and can be applied in the regime where a straightforward calculation of Feynman diagrams fails to give an answer. We show results for the simple though representative example of $\phi^4$ theory in non-perturbative parameter regimes. [Preview Abstract] |
Monday, March 13, 2017 3:30PM - 3:42PM |
C8.00006: Quantum Monte Carlo calculation of sp-bonded carbon chains: carbynes and carbon rings Iue Gyun Hong, Jeonghwan Ahn, Hyeonhu Bae, Hyeondeok Shin, Sungjin Park, Hoonkyung Lee, Anouar Benali, Yongkyung Kwon Both density functional theory (DFT) and quantum Monte Carlo (QMC) methods have been employed to study ground state properties of two forms of sp-bonded carbon chains: carbynes and carbon rings. According to the DFT-PBE calculations, polyyne, a carbyne structure with alternating single and triple C-C bonds, is energetically favored by 14 meV/atom over cumulene only with double bonds. However, our QMC calculations predict an energy difference of 88(4) meV/atom between them, clearly demonstrating that polyyne is the ground-state structure of carbyne. In the study of carbon rings consisting of 4n and (4n+2) C atoms, DFT calculations show electrons to be delocalized even in the regime where dimerization effects should be large. In contrast, for n>4, QMC calculations indicate the greater stability of a Peierls insulator configuration over a ground state predicted by Huckel’s rule. This qualitative difference between QMC and DFT results shows that many-body correlation effects taken into account by the QMC method are necessary to accurately describe even simple carbon systems such as sp-bonded carbon chains. [Preview Abstract] |
Monday, March 13, 2017 3:42PM - 3:54PM |
C8.00007: An accurate, compact and computationally efficient representation of orbitals for quantum Monte Carlo calculations Ye Luo, Kenneth Esler, Paul Kent, Luke Shulenburger Quantum Monte Carlo (QMC) calculations of giant molecules, surface and defect properties of solids have been feasible recently due to drastically expanding computational resources. However, with the most computationally efficient basis set, B-splines, these calculations are severely restricted by the memory capacity of compute nodes. The B-spline coefficients are shared on a node but not distributed among nodes, to ensure fast evaluation. A hybrid representation [1] which incorporates atomic orbitals near the ions and B-spline ones in the interstitial regions offers a more accurate and less memory demanding description of the orbitals because they are naturally more atomic like near ions and much smoother in between, thus allowing coarser B-spline grids. We will demonstrate the advantage of hybrid representation over pure B-spline and Gaussian basis sets and also show significant speed-up like computing the non-local pseudopotentials with our new scheme. Moreover, we discuss a new algorithm for atomic orbital initialization which used to require an extra workflow step taking a few days. With this work, the highly efficient hybrid representation paves the way to simulate large size even in-homogeneous systems using QMC. [1] K.P. Esler et al., Comput. Sci. Eng. 14, 40 (2012). [Preview Abstract] |
Monday, March 13, 2017 3:54PM - 4:06PM |
C8.00008: The pseudo Hamiltonian approach for effective atoms in Difussion Monte Carlo revisited Fernando Reboredo, Jaron Krogel Pseudo-Hamiltonians were initially proposed[1] as a method for removing computationally costly core electrons from diffusion Monte Carlo (DMC) calculations with purely differential operators. The approach, however, was largely abandoned. Pseudo-Hamiltonians were claimed to be very difficult to obtain specifically for transition elements. Instead, non-local pseudopotentials with the standard form used in single particle electronic structure have been used with relative success using the locality and later the T-moves approximations. However, these approximations give rise to systematic errors, in addition to the fixed-node, that largely depend on the quality of the trial wave function used to guide the DMC run. Since pseudo-Hamiltonians do not present those localization errors, we have revisited the idea for the case of transition metal ions. In this presentation we will discuss the cost and benefits of a pseudo-Hamiltonian treatment of the 3d Sc-Zn atomic series. [1] G. B. Bachelet, D. M. Ceperley, and M. G. B. Chiocchetti Phys. Rev. Lett. 62, 2088 (1989). [Preview Abstract] |
Monday, March 13, 2017 4:06PM - 4:18PM |
C8.00009: Variationally Optimized Slater-Jastrow Wave Functions for Constrained Path Quantum Monte Carlo Jeong-Pil Song, Leonard Sprague, Chia-Chen Chang, Brenda Rubenstein Real space Quantum Monte Carlo techniques, such as Diffusion Monte Carlo, have long employed optimized Slater-Jastrow wave functions as starting points for more accurate calculations. In this work, we present Constrained Path Quantum Monte Carlo calculations on the two-dimensional Hubbard model that make use of variationally optimized Slater-Jastrow trial wave functions. The Jastrow factors employed are determined through a stochastic optimization technique, as first pioneered for the variational optimization of tensor network states. The stability and accuracy of the algorithm with respect to the size of the variational parameter space are assessed. The systematic and statistical errors of the CPMC results obtained are compared to those obtained using mean field wave functions and unoptimized multideterminant expansions. We end with a discussion of how this algorithm can be generalized to produce optimized wave functions to be used as starting points for electronic structure calculations performed with Auxiliary Field Quantum Monte Carlo. [Preview Abstract] |
Monday, March 13, 2017 4:18PM - 4:30PM |
C8.00010: High-Performance Algorithm for Calculating Energy Level Densities in Many-Body Systems Roman Senkov, Vladimir Zelevinsky An algorithm using methods of statistical spectroscopy was developed for calculating level densities in quantum many-body systems. The approach is based on the ideas of complexity and quantum chaos and does not require diagonalization of large matrices. The algorithm was applied to the calculation of nuclear level densities in the proton-neutron formalism. This method was further improved to remove the contributions of spurious states. We show the results for some medium-mass nuclei and compare them with the exact shell-model level density. The method can be also used to extract with good precision the ground state energy for very large shell-model cases. The algorithm can be applied to other many-body systems with strong interaction. [Preview Abstract] |
Monday, March 13, 2017 4:30PM - 4:42PM |
C8.00011: Maxima of many body wave functions as a way to classify and visualize correlated physics William Wheeler, Lucas K. Wagner Correlated wave functions are difficult to visualize because of their high dimensionality. Often the effects of correlation are not strongly reflected in one particle quantities like the electron density. Inspired by recent work by Luechow [1], we investigate whether the local maxima of wave functions can offer insight into correlated physics. We find that even for bulk systems, the behavior of the maxima is relatively simple and offers an intuitive picture of the role of correlation in these wave functions. We also find that the local energy is a useful quantity to use to find clusters of local maxima. These clusters allow us to classify the maxima and further understand the wave function. [1] Luechow, J. Comput. Chem. 35, 854 (2014). [Preview Abstract] |
Monday, March 13, 2017 4:42PM - 4:54PM |
C8.00012: An ab initio approach to the origin of superexchange Alexander Munoz, Lucas K. Wagner The superexchange mechanism is the traditional explanation for antiferromagnetic couplings between magnetic ions. In this theory, the energy savings within the context of a hopping model is derived from kinetic energy terms. Our study focuses on determining, from ab initio calculations, whether the origin of interactions in magnetic systems~is explainable through the conventional arguments. Using quantum Monte Carlo, we investigate the model system (Mn-O-Mn)$^{\mathrm{+2}}$ where we will report on progress establishing the ab initio explanation for superexchange. We will focus on elucidating the ab initio calculated correlators and the effective model energy savings that result in an antiferromagnetic interaction in this system. [Preview Abstract] |
Monday, March 13, 2017 4:54PM - 5:06PM |
C8.00013: Equivalence of exchange - correlation functionals for the inhomogeneous electron gas and jellium at finite temperature James Dufty A common approximation or constraint in density functional theory is based on the equivalence of exchange - correlation functionals for uniform electrons and for jellium (uniform electrons with neutralizing background). It is shown here that this equivalence holds more generally for the inhomogeneous case as well. Related issues of the thermodynamic limit are noted. [Preview Abstract] |
Monday, March 13, 2017 5:06PM - 5:18PM |
C8.00014: Density Waves, Sub-Gap Structures, and Translational Invariance in Cluster Methods for cuprates Simon Verret, Maxime Charlebois, Alexandre Foley, David Sénéchal, A.-M. S. Tremblay Cluster Dynamical Mean-Field Theory (CDMFT) is widely used to solve the two-dimensional Hubbard model and explain key features of high temperature superconductors (cuprates) [1]. However, it is known that this numerical method intrinsically breaks translational invariance, a problem usually addressed through various periodization schemes [2]. Yet, in light of the massive experimental evidence for bulk density waves in cuprates, translational-symmetry breaking seems to play an important role in any theory for the cuprates. Is it possible that artificially breaking translational invariance may actually help CDMFT to deal with the cuprate problem? In this talk we analyze the effects of translational-symmetry breaking intrinsic to CDMFT and find much similarity with charge-density waves and pair-density waves mean-fields. Based on this knowledge, we discuss avenues to improve CDMFT. --- [1] Lichtenstein and Katsnelson PRB 62 R9283 (2000); Kotliar et al. PRL 87 186401 (2001); Maier et al. RMP 77 1027 (2005). [2] Kancharla et al. PRB 77 184516 (2008); Biroli et al. PRB 69 205108 (2004); Sakai et al. PRB 85 35102 (2012). [Preview Abstract] |
Monday, March 13, 2017 5:18PM - 5:30PM |
C8.00015: Energy gap of neutral excitations implies vanishing charge susceptibility Haruki Watanabe In quantum many-body systems with a U(1) symmetry, such as the particle number conservation and the axial spin conservation, there are two distinct types of excitations: charge-neutral excitations and charged excitations. The energy gaps of these excitations may be independent with each other in strongly correlated systems. The static susceptibility of the U(1) charge vanishes when the charged excitations are all gapped, but its relation to the neutral excitations is not obvious. In this talk, we show that a finite excitation gap of the neutral excitations is, in fact, sufficient to prove that the charge susceptibility vanishes (i.e. the system is incompressible). This result gives a partial explanation on why the celebrated quantization condition that $n(S-m_z)$ must be an integer at magnetization plateaus works even in spatial dimensions greater than one. Ref: arXiv:1609.09543 [Preview Abstract] |
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