Rigorous results concerning the Holstein-Hubbard model
This paper deals with the study of the Holstein-Hubbard model with repulsive Coulomb interactions. The methods developed in this paper require a restriction on the electron-photon coupling strength. By using the Lang-Firsov transformations, the author establishes several expressions of the Hamiltonian. Next, by choosing a suitable Hilbert cone, it is proved that the heat semi-group generated by the Hamiltonian preserves the positivity. A central result of this paper concerns the uniqueness of the ground state, which follows by using the Faris theorem (a generalized version of the Perron-Frobenius theorem). In the final part of this paper, by extending the method of Gaussian domination, an upper bound on the charge susceptibility is deduced. Three appendices provide some additional results used in the paper and the proof of a technical property which is used in the proof of the main result.
scientific article; zbMATH DE number 6688788
scientific article