Comparison of the iterated equation of motion approach and the density matrix formalism for the quantum Rabi model
Lehrstuhl für Theoretische Physik I, TU Dortmund, Otto-Hahn Straße 4, 44221 Dortmund, Germany
Received: 25 January 2017
Received in final form: 28 March 2017
Published online: 24 May 2017
The density matrix formalism and the equation of motion approach are two semi-analytical methods that can be used to compute the non-equilibrium dynamics of correlated systems. While for a bilinear Hamiltonian both formalisms yield the exact result, for any non-bilinear Hamiltonian a truncation is necessary. Due to the fact that the commonly used truncation schemes differ for these two methods, the accuracy of the obtained results depends significantly on the chosen approach. In this paper, both formalisms are applied to the quantum Rabi model. This allows us to compare the approximate results and the exact dynamics of the system and enables us to discuss the accuracy of the approximations as well as the advantages and the disadvantages of both methods. It is shown to which extent the results fulfill physical requirements for the observables and which properties of the methods lead to unphysical results.
Key words: Solid State and Materials
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2017