Asymptotic fourth-order time-convolutionless generator for the spin-boson model: Analytical derivation and benchmarking
Phys. Rev. B 113, 045404 – Published 2 January, 2026
DOI: https://doi.org/10.1103/69y3-x6vh
Abstract
The spin-boson model is a widely used model for understanding the properties of a two-level open quantum system. Accurately describing its dynamics often requires going beyond the weak system-environment coupling approximation. However, calculating the higher-order generators of such dynamics, with a system-environment coupling that is not too weak, has been known to be challenging, both numerically and analytically. This work presents the analytical derivation of the complete fourth-order time-convolutionless (TCL) generator for a generic spin-boson model, accurate up to fourth order in the system-environment coupling parameter for a broad class of environmental spectral densities. In the case of a semiconductor double-quantum-dot system, our results reveal corrections to the dynamics that may become physically significant in some parameter regimes. Within the regime of its applicability, our results provide a computational advantage over numerically exact techniques and can be applied to a wide class of nanomaterial and condensed matter systems like superconducting qubits, as well as in fields like quantum information, computing, and thermodynamics. Furthermore, we report that the widely used second-order TCL master equation tends to overestimate the non-Markovianity of a dynamics over a large parameter regime. The accuracy of the fourth-order TCL generator is rigorously benchmarked against specialized analytical calculations done for the Ohmic spectral density with Drude cutoff and against the numerically exact hierarchical equations of motion technique.
