Bulletin of the American Physical Society
APS March Meeting 2021
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session F21: Precision ManyBody Physics I: Methods and AlgorithmsFocus Live

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Sponsoring Units: DCOMP DCMP DAMOP Chair: Joaquin Drut, University of North Carolina at Chapel Hill 
Tuesday, March 16, 2021 11:30AM  11:42AM 
F21.00001: Quantum QuasiMonte Carlo Technique for ManyBody 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 manybody systems, even at strong coupling. We adapt integration methods using lowdiscrepancy sequences to this problem. They greatly outperform stateoftheart diagrammatic Monte Carlo simulations. In practical applications, we show speedups of several orders of magnitude with scaling as fast as 1/N in sample number N; parametrically faster than 1/N^{1/2} 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 Realtime 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/N^{0.5}). In recent work, we replaced the Metropolis algorithm and adapted DiagQMC to a QuasiMonte 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 speedups of several orders of magnitude for favourable parameters. 
Tuesday, March 16, 2021 11:54AM  12:06PM 
F21.00003: Highorder 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 gapfunction equation. However, within the implicit renormalization approach, the gapfunction 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 fourpoint 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 imaginarytime quantum manybody simulations Mancheon Han, Hyoung Joon Choi In manybody physics, causality often refers to positive semidefiniteness of electronic spectral function. However, most numerical simulations of manyparticle systems are performed in imaginary time, without any explicit consideration for causality. In this work, we present a causal projection approach which projects an imaginarytime numerical function onto a space of functions satisfying causality. Using this method, we can impose causality in imaginarytime manybody calculations. Applying this method to finite and statistical calculations, we demonstrate that causality determines intermediatefrequency behaviors smoothly, excluding unphysical statistical errors efficiently. Furthermore, we show that our causal projection method can suppress unphysical branches of the LuttingerWard functional. 
Tuesday, March 16, 2021 12:42PM  12:54PM Live 
F21.00007: Exact SelfConsistent Effective Hamiltonian Theory Xindong Wang, Xiao Chen, Liqin Ke, HaiPing Cheng, Bruce Harmon Exact solutions to interacting manybody fermionic systems, especially in dimensions higher than one, have always been the holy grail for quantum physicists. Computationally, the exponential growth of the FockHilbert 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 manybody 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 selfconsistent 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 manybody problem by decoupling manybody propagators into integrals over onebody problems to which noninteracting 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 HStransformed operators to implement algorithms will motivate other methods and anticipate that our technique will enable direct performance comparisons against other manybody approaches formulated in the CE. 
Tuesday, March 16, 2021 1:06PM  1:42PM Live 
F21.00009: DMRG Approach to Optimizing TwoDimensional Tensor Networks Invited Speaker: Katharine Hyatt Tensor network algorithms have been remarkably successful solving a variety of problems in quantum manybody physics. However, algorithms to optimize twodimensional tensor networks known as PEPS lack many of the aspects that make the seminal density matrix renormalization group (DMRG) algorithm so powerful for optimizing onedimensional tensor networks known as matrix product states. We implement a framework for optimizing twodimensional PEPS tensor networks which includes all of steps that make DMRG so successful for optimizing onedimension 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: HighOrder Renormalized Perturbative Approach for StronglyCorrelated 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 highenergy 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. 
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