Density matrix renormalization group approach of the spin-boson model

TL;DR

This paper introduces a density matrix renormalization group method for analyzing the spin-boson model, effectively identifying phase transitions and comparing favorably with existing numerical approaches.

Contribution

It develops a DMRG-based approach with an optimized phonon scheme for the spin-boson model, enabling analysis of large phonon baths and phase transition points.

Findings

Accurately determines delocalized-localized transition points.

Shows good agreement with NRG results in Ohmic and sub-Ohmic cases.

Provides a scalable method for large bosonic environments.

Abstract

We propose a density matrix renormalization group approach to tackle a two-state system coupled to a bosonic bath with continuous spectrum. In this approach, the optimized phonon scheme is applied to several hundred phonon modes which are divided linearly among the spectrum. Although DMRG cannot resolve very small energy scales, the delocalized-localized transition points of the two-state system are extracted by the extrapolation of the flow diagram results. The phase diagram is compared with the numerical renormalization group results and shows good agreement in both Ohmic and sub-Ohmic cases.