The spectral density of the Rabi model is calculated exactly within a continued-fraction approach. It is shown that the method provides a simple algorithm for the spectral density with convergent solutions. We compare these recursive solutions with the solutions of the Jaynes–Cummings model and discuss the effect of approximations on the spectral properties.

arXiv:1204.3856Journal of Physics A Mathematical and TheoreticalOct 18, 201214 citations

Thermodynamical properties of quantum many-body systems

Eduardo R. Gagliano, S. Bacci

We present a method to compute exactly the partition function of quantum many-body systems. This approach involves the evaluation of a set of coefficients for the continued-fraction expansion of a resolventlike operator. The main advantage of this method is that this set of coefficients is unique and allows one to calculate the partition function at any temperature. As an illustration, the method is applied to a simple one-dimensional spinless model.

Physical Review LettersMar 6, 19895 citations

Annals of Physics

Convergence properties of methods for effective operator calculations studied in a simple many-body model

Jon Magne Leinaas, T.T.S. Kuo

Published May 1, 1976• 18 citations

Publisher

DOI: 10.1016/0003-4916(76)90243-8

Related papers

Convergence properties of methods for effective operator calculations studied in a simple many-body model

Annals of PhysicsMar 1, 19760 citations

Validity of many-body approximation methods for a solvable model

Dan Agassi, Harry J. Lipkin, N. Meshkov

Nuclear PhysicsOct 1, 1966122 citations

Unitary correlation operator method and similarity renormalization group: Connections and differences

Robert Roth, S. Reinhardt, H. Hergert

We discuss relations and differences between two methods for the construction of unitarily transformed effective interactions, the Similarity Renormalization Group (SRG) and Unitary Correlation Operator Method (UCOM). The aim of both methods is to construct a soft phase-shift equivalent effective interaction which is well suited for many-body calculations in limited model spaces. After contrasting the two conceptual frameworks, we establish a formal connection between the initial SRG-generator and the static generators of the UCOM transformation. Furthermore we propose a mapping procedure to extract UCOM correlation functions from the SRG evolution. We compare the effective interactions resulting from the UCOM-transformation and the SRG-evolution on the level of matrix elements, in no-core shell model calculations of light nuclei, and in Hartree-Fock calculations up to $^{208}\mathrm{Pb}$ . Both interactions exhibit very similar convergence properties in light nuclei but show a different systematic behavior as function of particle number.We discuss relations and differences between two methods for the construction of unitarily transformed effective interactions, the Similarity Renormalization Group (SRG) and Unitary Correlation Operator Method (UCOM). The aim of both methods is to construct a soft phase-shift equivalent effective interaction which is well suited for many-body calculations in limited model spaces. After contrasting the two conceptual frameworks, we establish a formal connection between the initial SRG-generator and the static generators of the UCOM transformation. Furthermore we propose a mapping procedure to extract UCOM correlation functions from the SRG evolution. We compare the effective interactions resulting from the UCOM-transformation and the SRG-evolution on the level of matrix elements, in no-core shell model calculations of light nuclei, and in Hartree-Fock calculations up to $^{208}\mathrm{Pb}$. Both interactions exhibit very similar convergence properties in light nuclei but show a different systematic behavior as function of particle number.

arXiv:0802.4239Physical Review CJun 20, 200876 citations

Validity of many-body approximation methods for a solvable model

N. Meshkov, Arnold J. Glick, Harry J. Lipkin

Nuclear PhysicsFeb 1, 1965363 citations

Short note on the Rabi model

K. Ziegler

arXiv:1204.3856Journal of Physics A Mathematical and TheoreticalOct 18, 201214 citations

Thermodynamical properties of quantum many-body systems

Eduardo R. Gagliano, S. Bacci

Physical Review LettersMar 6, 19895 citations

^{208}\mathrm{Pb}

. Both interactions exhibit very similar convergence properties in light nuclei but show a different systematic behavior as function of particle number.