Quantum and semiclassical dynamics of a two-level system coupled to a bosonic degree of freedom

Exact real-time dynamics of the quantum Rabi model

“…Although the lower part of the spectrum of the QRM can be computed numerically to arbitrary precision using exact diagonalization on a truncated state space due to the convergence properties of the associated continued fraction [6][7][8][9], it is by no means evident whether the properties of the numerically obtained eigenstates correspond to those of the true eigenstates of the untruncated model. Even if the spectra of the truncated and the full model are close for a subset of the eigenvalues, the corresponding eigenvectors could still be related by a unitary transformation, which does not necessarily approach the identity.…”

Continued fractions and the Rabi model

“…The spectral condition on H N provides an approximation to the spectrum of the full model precisely because it approximates the exact condition of analyticity in the Bargmann space. It follows that the continued fraction approach initiated by Schweber and pursued by several authors [7][8][9][10][11] can be used to obtain the spectrum of the quantum Rabi model to arbitrary precision. The method does not use the Z 2 -symmetry of H R as the Bargmann condition is implemented via (5).…”

“…The approach based on the symmetry of the model leads in this way to a unified picture of all spectral properties. Independent from the qualitative understanding of the physics governing the quantum Rabi model is the question whether the analytical solution could invalidate the widely used numerical determination of the spectrum through exact diagonalization on a truncated state space, or the equivalent continued fraction techniques [5][6][7][8][9][10][11][12]. There has been recent confusion on this point [13,14] and the present paper intends to clarify the situation regarding the methods based on continued fractions.…”