Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory

TL;DR

This paper introduces a novel analytical method based on unitary perturbation theory for studying real-time evolution in quantum many-body systems, enabling stable long-term analysis without secular divergences.

Contribution

It generalizes classical canonical perturbation theory to quantum systems, providing a systematic approach to avoid secular terms and analyze non-equilibrium dynamics.

Findings

Applied to the spin-boson model to analyze spin dynamics

Achieved stable long-time evolution predictions

Demonstrated effectiveness in non-equilibrium scenarios

Abstract

We develop a new analytical method for solving real time evolution problems of quantum many-body systems. Our approach is a direct generalization of the well-known canonical perturbation theory for classical systems. Similar to canonical perturbation theory, secular terms are avoided in a systematic expansion and one obtains stable long-time behavior. These general ideas are illustrated by applying them to the spin-boson model and studying its non-equilibrium spin dynamics.