Taming the dynamical sign problem in real-time evolution of quantum many-body problems

TL;DR

The paper introduces the Inchworm Algorithm, a novel approach that significantly reduces the dynamical sign problem in real-time quantum many-body simulations, enabling longer and more accurate simulations.

Contribution

It presents the Inchworm Algorithm, which reuses previous information to extend real-time quantum simulations, reducing computational complexity from exponential to quadratic.

Findings

Successfully applied to the Anderson impurity model in various regimes.

Achieved longer simulation times with reduced computational cost.

Demonstrated accurate results for quenches and spin dynamics under magnetic fields.

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.