Dynamical renormalization group approach to the spin-boson model

TL;DR

This paper introduces a semi-analytical dynamical renormalization group method to study the strong-coupling quench dynamics of the spin-boson model, extending beyond traditional approximations.

Contribution

It develops a novel time-dependent renormalization group approach that captures non-Markovian dynamics in the spin-boson model at strong coupling.

Findings

The method agrees well with NRG calculations.

It accurately reproduces non-interacting blip approximation results.

Provides a new framework for real-time dynamics in open quantum systems.

Abstract

We develop a semi-analytical approach beyond the Born-Markov approximation to study the quench dynamics of the spin-boson model in the strong-coupling regime ($\alpha\leq1/2$) for the Ohmic bath. The basic idea in our approach is to write an effective time-dependent model for the dynamics of the system coupled to the bosonic bath after integrating out high-frequency bath modes. By applying this procedure to the Heisenberg equations of motion, we derive a set of flow equations for the system parameters as a function of time. The final flow equations look similar to those of the equilibrium renormalization-group theory; however, in our derivation the scaling parameter is set by the real time. We solve the equations of motion with time-dependent renormalized parameters and show that the resulting dynamics is in decent agreement with the exact NRG calculations as well as the non-interacting blip approximation that is a well-known good solution in this limit.