Exact solution of a polaron model in one dimension

X.-W. Guan, Heng Fan, S.-D. Yang

Hiroyuki Kaga

Sergio Ciuchi, FERDINANDO DE PASQUALE, D. Feinberg

The spectral function of a single electron coupled to Einstein phonons (Holstein model) is calculated exactly in the limit of large space dimensionality, for any coupling strength and phonon frequency. A self-consistent mapping onto an effective impurity model leads to the solution in terms of a continued-fraction expansion for the electron propagator at zero temperature. True self-trapping is obtained only for finite bandwidth, such as the case of a Bethe lattice in infinite dimensions. It is shown that at intermediate coupling multiphonon resonances develop, corresponding to polaron states. Only the lowest one has long lifetime, and the polaron mass is calculated.

Petar Mitrić, Veljko Janković, Nenad Vukmirović +1 more

It is generally accepted that the dynamical mean field theory gives a good solution of the Holstein model, but only in dimensions greater than two. Here, we show that this theory, which becomes exact in the weak coupling and in the atomic limit, provides an excellent, numerically cheap, approximate solution for the spectral function of the Holstein model in the whole range of parameters, even in one dimension. To establish this, we make a detailed comparison with the spectral functions that we obtain using the newly developed momentum-space numerically exact hierarchical equations of motion method, which yields electronic correlation functions directly in real time. We crosscheck these conclusions with our path integral quantum Monte Carlo and exact diagonalization results, as well as with the available numerically exact results from the literature.

J. Röseler, Michael Hartmann

Александр Иванович Волокитин