A new approximating method for holstein model

Motoyuki Sato, Kosuke Takada

When the Holstein-Primakoff (Hermitian)-type boson expansion theory is applied for nuclear structure calculations, truncation at the fourth-order expansion of the boson Hamiltonian is often used. The Dyson-type boson mapping has no difficulty concerning boson expansion, since the Dyson boson Hamiltonian is written in up to sixth-order boson operators, and we do not have to make any truncation of the boson expansion. In the present work, we propose a new clear-cut method to obtain the normal-ordered Holstein-Primakoff boson expansion. Using this method, we test whether or not the truncation of the boson expansion is good approximation in various cases. We show that truncation at the fourth-order expansion of the normal-ordered Holstein-Primakoff boson Hamiltonian is a rather good approximation, but it is not sufficient for detailed analyses.

Chunli Zhang

Glen L. Goodvin, Andrei S. Mishchenko, Mona Berciu

The momentum average approximation is used to derive a new kind of nonperturbational analytical expression for the optical conductivity (OC) of a Holstein polaron at zero temperature. This provides insight into the shape of the OC, by linking it to the structure of the polaron's phonon cloud. Our method works in any dimension, properly enforces selection rules, can be systematically improved, and also generalizes to momentum-dependent couplings. Its accuracy is demonstrated by a comparison with the first detailed set of three-dimensional numerical OC results, obtained using the approximation-free diagrammatic Monte Carlo method.

Chuang Chen, Xiao Yan Xu, Junwei Liu +3 more

P. Benedetti, R. Zeyher

F. Marsiglio

We study the two-dimensional Holstein model at half-filling for small systems using quantum Monte Carlo methods and through diagrammatic perturbation techniques in the Migdal-Eliashberg approximation. It is found that the latter approximation is very accurate as long as the phonon self-energy is taken into account in a self-consistent way. Vertex corrections are not required.