Rigorous results concerning the Holstein-Hubbard model
type: Item
instance of: scholarly article
title: Rigorous results concerning the Holstein-Hubbard model
zbMATH Open document ID: 1361.82036
author: Tadahiro Miyao
published in: Annales Henri Poincaré
publication date: 2017-02-24T00:00:00Z
review text: 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.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 82D20
Mathematics Subject Classification ID: 82C22
Mathematics Subject Classification ID: 82D55
zbMATH DE Number: 6688788
zbMATH Keywords: Holstein-Hubbard model
zbMATH Keywords: Coulomb interactions
zbMATH Keywords: ground state
zbMATH Keywords: Hilbert cones
MaRDI profile type: Publication
full work available at URL: s00023-016-0506-5
OpenAlex ID: W2381624779
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DOI: 10.1007/S00023-016-0506-5
description: scientific article; zbMATH DE number 6688788