Monte Carlo study of real time dynamics

TL;DR

This paper introduces a novel Monte Carlo method for real-time quantum dynamics using path integral deformation to mitigate the sign problem, demonstrated on an anharmonic oscillator.

Contribution

A new approach deforming the integration domain to a complex manifold for Monte Carlo simulations of real-time dynamics, applicable to quantum field theory.

Findings

Results agree with exact diagonalization for the anharmonic oscillator

Method reduces phase oscillations and sign problem severity

Potential for extension to quantum field theory

Abstract

Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from highly oscillatory phase of the path integral. In this letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced "contraction algorithm" to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and in principle applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm.