Comparison of the iterated equation of motion approach and the density matrix formalism for the quantum Rabi model

Abstract

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. PACS. 02.30.Mv Approximations and expansions -02.60.Cb Numerical simulation; solution of equations -05.30.Jp Boson systems arXiv:1701.07282v3 [cond-mat.str-el]

Strong quenches in the one-dimensional Fermi-Hubbard model

“…The respective maximum times are given by the three different plot symbols. Triangles at the x-axis mark predictions for zeros of the curve based on the Rabi oscillations (46).…”

Momentum-resolved analysis of condensate dynamic and Higgs oscillations in quenched superconductors with time-resolved ARPES

“…where the HamiltonianH (t ), α † k (t ) and β † k (t ) are the operators in the Heisenberg picture. To evaluate these equations, we make use of the iterated equation of motion approach [42] to write the Bogoliubov operators in the Heisenberg picture as a time-dependent superposition of the equilibrium operators…”

Charge dynamics in magnetically disordered Mott insulators

“…In order to deduce the full energy spectrum and the lower band edge in particular we resort to the iterated equations of motion approach [39][40][41], a brief summary of which is given in the first part of this section. The second part is dedicated to the necessary modifications of the method which warrant a unitary time evolution on the operator level [27,28], and the third part describes the concrete application of the iEoM to the t-J model.…”

“…It has been previously shown [27,28] that it is crucial to achieve Hermiticity of M, i.e., preserving the property M ji = M * ij in order to obtain oscillatory solutions. Otherwise, exponentially increasing solutions are possible and will occur.…”

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