Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session F21: Precision Many-Body Physics I: Methods and AlgorithmsFocus Live
|
Hide Abstracts |
Sponsoring Units: DCOMP DCMP DAMOP Chair: Joaquin Drut, University of North Carolina at Chapel Hill |
Tuesday, March 16, 2021 11:30AM - 11:42AM Live |
F21.00001: Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions Marjan Maček, Philipp Dumitrescu, Corentin Bertrand, Bill Triggs, Olivier Parcollet, Xavier Waintal High order perturbation theory has seen an unexpected recent revival for controlled calculations of quantum many-body systems, even at strong coupling. We adapt integration methods using low-discrepancy sequences to this problem. They greatly outperform state-of-the-art diagrammatic Monte Carlo simulations. In practical applications, we show speed-ups of several orders of magnitude with scaling as fast as 1/N in sample number N; parametrically faster than 1/N1/2 in Monte Carlo simulations. We illustrate our technique with a solution of the Kondo ridge in quantum dots, where it allows large parameter sweeps. |
Tuesday, March 16, 2021 11:42AM - 11:54AM Live |
F21.00002: Quantum Monte Carlo without random numbers Marjan Maček, Philipp Dumitrescu, Corentin Bertrand, Bill Triggs, Olivier Parcollet, Xavier Waintal Real-time diagrammatic quantum Monte Carlo (DiagQMC) is one of the few methods able to treat quantum impurity problem out of equilibrium. Like all Monte Carlo methods, it remains hindered by a convergence rate of one over square root of the number of calculated points (1/N0.5). In recent work, we replaced the Metropolis algorithm and adapted DiagQMC to a Quasi-Monte Carlo integration method, where integration is performed using deterministic low discrepancy sequences [1]. We obtained convergence rate of one over the number of calculated points (1/N) and showed speed-ups of several orders of magnitude for favourable parameters. |
Tuesday, March 16, 2021 11:54AM - 12:06PM Live |
F21.00003: High-order expansion around BCS theory Gabriele Spada, Riccardo Rossi, Fedor Simkovic, Renaud Garioud, Michel Ferrero, Kris Van Houcke, Félix Werner In contrast to conventional QMC methods, expansions of intensive quantities in series of connected Feynman diagrams can be formulated directly in the thermodynamic limit. Over the last decade, new Monte Carlo algorithms made it possible to reach large expansion orders and to obtain accurate results for various key models of interacting fermions in previously inaccessible regimes. |
Tuesday, March 16, 2021 12:06PM - 12:18PM Live |
F21.00004: Implicit renormalization approach to the problem of Cooper instability Nikolai Prokof'ev, Andrey Chubukov, Boris Svistunov In the vast majority of cases, superconducting transition takes place at exponentially low temperature Tc out of the Fermi liquid regime. We discuss the problem of determining Tc from known system properties at temperatures T >> Tc, and stress that this cannot be done reliably by following the standard protocol of solving for the largest eigenvalue of the original gap-function equation. However, within the implicit renormalization approach, the gap-function equation can be used to formulate an alternative eigenvalue problem, solving which leads to an accurate prediction for both Tc and the gap function immediately below Tc. With the diagrammatic Monte Carlo techniques, this eigenvalue problem can be solved without invoking the matrix inversion or even explicitly calculating the four-point vertex function. [Phys. Rev. B 100, 064513 (2019)] |
Tuesday, March 16, 2021 12:18PM - 12:30PM Live |
F21.00005: Evaluation of arbitrary Feynman graphs via algorithmic methods. James LeBlanc Feynman diagrammatics is a powerful tool for the study of correlated electron systems. |
Tuesday, March 16, 2021 12:30PM - 12:42PM Live |
F21.00006: Causal projection approach for imaginary-time quantum many-body simulations Mancheon Han, Hyoung Joon Choi In many-body physics, causality often refers to positive semidefiniteness of electronic spectral function. However, most numerical simulations of many-particle systems are performed in imaginary time, without any explicit consideration for causality. In this work, we present a causal projection approach which projects an imaginary-time numerical function onto a space of functions satisfying causality. Using this method, we can impose causality in imaginary-time many-body calculations. Applying this method to finite and statistical calculations, we demonstrate that causality determines intermediate-frequency behaviors smoothly, excluding unphysical statistical errors efficiently. Furthermore, we show that our causal projection method can suppress unphysical branches of the Luttinger-Ward functional. |
Tuesday, March 16, 2021 12:42PM - 12:54PM Live |
F21.00007: Exact Self-Consistent Effective Hamiltonian Theory Xindong Wang, Xiao Chen, Liqin Ke, Hai-Ping Cheng, Bruce Harmon Exact solutions to interacting many-body fermionic systems, especially in dimensions higher than one, have always been the holy grail for quantum physicists. Computationally, the exponential growth of the Fock-Hilbert space's dimension with the size of the system (number of fermions, for example) also makes it a benchmark problem for quantum computations. We propose a general variational fermionic many-body wavefunction that generates an effective Hamiltonian in a quadratic form, which can then be exactly solved. The theory can be constructed within the density functional theory framework, and a self-consistent scheme is proposed for solving the exact density functional theory. Numerical algorithm based on the theory and results on some prototype systems are presented to illustrate the potential of the theory. |
Tuesday, March 16, 2021 12:54PM - 1:06PM Live |
F21.00008: Finite Temperature Auxiliary Field Quantum Monte Carlo in the Canonical Ensemble Tong Shen, Yuan Liu, Brenda M Rubenstein In this work, we present a new recursive approach for performing Auxiliary Field Quantum Monte Carlo (AFQMC) in the canonical ensemble (CE) that does not require knowledge of chemical potentials. Unlike previous CE algorithms, which relied upon projecting CE properties out from grand canonical simulations, our formalism eliminates the costly need to scan through chemical potentials to fix average particle numbers, enabling efficient and more accurate treatments for systems with fixed particle numbers. To derive this approach, we exploit the fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms will motivate other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the CE. |
Tuesday, March 16, 2021 1:06PM - 1:42PM Live |
F21.00009: DMRG Approach to Optimizing Two-Dimensional Tensor Networks Invited Speaker: Katharine Hyatt Tensor network algorithms have been remarkably successful solving a variety of problems in quantum many-body physics. However, algorithms to optimize two-dimensional tensor networks known as PEPS lack many of the aspects that make the seminal density matrix renormalization group (DMRG) algorithm so powerful for optimizing one-dimensional tensor networks known as matrix product states. We implement a framework for optimizing two-dimensional PEPS tensor networks which includes all of steps that make DMRG so successful for optimizing one-dimension tensor networks. We present results for several 2D spin models and discuss possible extensions and applications. |
Tuesday, March 16, 2021 1:42PM - 2:18PM Live |
F21.00010: High-Order Renormalized Perturbative Approach for Strongly-Correlated Fermions Invited Speaker: Riccardo Rossi In this talk I show how perturbation theory can be turned into a |
Tuesday, March 16, 2021 2:18PM - 2:30PM Live |
F21.00011: Solving the Bethe–Salpeter equation with exponential convergence Markus Wallerberger, Hiroshi Shinaoka, Anna Kauch The Bethe–Salpeter equation plays a crucial role in understanding the physics of correlated fermions, relating to optical excitations in solids and molecules as well as resonances in high-energy physics. Yet it is notoriously difficult to control numerically, typically requiring an effort that scales polynomially with energy scales and accuracy. This puts many interesting systems out of computational reach. |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700