Taming the Dynamical Sign Problem in Real-Time Evolution of Quantum Many-Body Problems

Physical Review Letters
Guy CohenAndrew J Millis

Abstract

Current nonequilibrium Monte Carlo methods suffer from a dynamical sign problem that makes simulating real-time dynamics for long times exponentially hard. We propose a new "inchworm algorithm," based on iteratively reusing information obtained in previous steps to extend the propagation to longer times. The algorithm largely overcomes the dynamical sign problem, changing the scaling from exponential to quadratic. We use the method to solve the Anderson impurity model in the Kondo and mixed valence regimes, obtaining results both for quenches and for spin dynamics in the presence of an oscillatory magnetic field.

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Citations

Apr 12, 2017·Chemical Society Reviews·Michael Galperin
Nov 30, 2019·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Denis ZhuravelSteffen Schäfer
Feb 10, 2017·The Journal of Chemical Physics·Hsing-Ta ChenDavid R Reichman
May 26, 2018·Physical Review Letters·Francesco PeronaciOlivier Parcollet
Aug 22, 2018·Nature Communications·A StrathearnB W Lovett
Sep 17, 2018·The Journal of Chemical Physics·Lyran KidonEran Rabani
Jun 24, 2019·The Journal of Chemical Physics·Amikam LevyDavid T Limmer
Jul 1, 2019·The Journal of Chemical Physics·Michael RidleyGuy Cohen
Feb 17, 2017·The Journal of Chemical Physics·Meng XuQiang Shi
Nov 15, 2016·Physical Review. E·Emilie Huffman, Shailesh Chandrasekharan
Feb 10, 2017·The Journal of Chemical Physics·Hsing-Ta ChenDavid R Reichman
Aug 3, 2019·The Journal of Chemical Physics·Marco Schiro, Orazio Scarlatella
Jun 4, 2020·The Journal of Chemical Physics·Arif UllahVladimir Chernyak
Jun 6, 2020·Physical Review Letters·Eitan EidelsteinGuy Cohen
Jan 22, 2018·The Journal of Chemical Physics·Michael Thoss, Ferdinand Evers
Apr 9, 2018·The Journal of Chemical Physics·YongXi ChengYiJing Yan
May 31, 2019·Physical Review Letters·Feng ChenMichael Galperin
Feb 10, 2018·The Journal of Chemical Physics·Joshua S Kretchmer, Garnet Kin-Lic Chan
Aug 17, 2020·Physical Review Letters·Marjan MačekXavier Waintal
Jan 23, 2021·The Journal of Chemical Physics·Guy Cohen, Michael Galperin
Mar 6, 2021·The Journal of Physical Chemistry Letters·Luis E Herrera Rodríguez, Alexei A Kananenka
Jul 10, 2021·The Journal of Chemical Physics·Matthew S Church, Brenda M Rubenstein
Jul 31, 2021·Physical Review Letters·Daniel KarlssonGianluca Stefanucci
Aug 4, 2021·The Journal of Chemical Physics·Erika Ye, Garnet Kin-Lic Chan
Aug 11, 2018·The Journal of Physical Chemistry Letters·Abraham Nitzan, Michael Galperin
Aug 31, 2019·Chemical Reviews·Yudong CaoAlán Aspuru-Guzik

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