TAMING THE DYNAMICAL SIGN PROBLEM: THE INCHWORM ALGORITHM

Molecular electronics systems and strongly correlated materials are often modeled by nonequilibrium quantum impurity models. Solution of such models in equilibrium has been dominated by quantum Monte Carlo (QMC) methods formulated in imaginary (or Matsubara) time. However, nonequilibrium QMC, which must be formulated in real time, suffers from a dynamical sign problem that makes simulating dynamics for long times exponentially hard. We propose a new "Inchworm Algorithm",¹ 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.

[1] Cohen, G., Gull, E., Reichman, D.R., Millis, A.J., 2015. Taming the dynamical sign problem in real-time evolution of quantum many-body problems. Physical Review Letters (in press).