A translation invariant $N$ -polaron system is investigated at arbitrary electron-phonon coupling strength, using a variational principle for path integrals for identical particles. An upper bound for the ground-state energy is found as a function of the number of spin up and spin down polarons, taking the electron-electron interaction and the Fermi statistics into account. The resulting addition energies and the criteria for multipolaron formation are discussed.A translation invariant $N$-polaron system is investigated at arbitrary electron-phonon coupling strength, using a variational principle for path integrals for identical particles. An upper bound for the ground-state energy is found as a function of the number of spin up and spin down polarons, taking the electron-electron interaction and the Fermi statistics into account. The resulting addition energies and the criteria for multipolaron formation are discussed.

arXiv:cond-mat/0601548Physical Review BJun 6, 200514 citations

Bounds on the minimal energy of translation invariant n-polaron systems

Marcel Griesemer, Jacob Schach Møller

For systems of N charged fermions (e.g. electrons) interacting with longi-tudinal optical quantized lattice vibrations of a polar crystal we derive upper and lower bounds on the minimal energy within the model of H. Fröhlich. The only parameters of this model, after removing the ultraviolet cutoff, are the constants U> 0 and α> 0 measuring the electron-electron and the electron-phonon coupling strengths. They are constrained by the condition 2α < U, which follows from the dependence of U and α on electrical properties of the crystal. We show that the large N asymptotic behavior of the minimal energy EN changes at 2α = U and that 2α ≤ U is necessary for ther-modynamic stability: for 2α> U the phonon-mediated electron-electron attraction overcomes the Coulomb repulsion and EN behaves like −N7/3. 2 M. Griesemer and J. S. Møller 1For systems of N charged fermions (e.g. electrons) interacting with longi-tudinal optical quantized lattice vibrations of a polar crystal we derive upper and lower bounds on the minimal energy within the model of H. Fröhlich. The only parameters of this model, after removing the ultraviolet cutoff, are the constants U> 0 and α> 0 measuring the electron-electron and the electron-phonon coupling strengths. They are constrained by the condition 2α < U, which follows from the dependence of U and α on electrical properties of the crystal. We show that the large N asymptotic behavior of the minimal energy EN changes at 2α = U and that 2α ≤ U is necessary for ther-modynamic stability: for 2α> U the phonon-mediated electron-electron attraction overcomes the Coulomb repulsion and EN behaves like −N7/3. 2 M. Griesemer and J. S. Møller 1

Aug 4, 201321 citations

A translation invariant

N

-polaron system is investigated at arbitrary electron-phonon coupling strength, using a variational principle for path integrals for identical particles. An upper bound for the ground-state energy is found as a function of the number of spin up and spin down polarons, taking the electron-electron interaction and the Fermi statistics into account. The resulting addition energies and the criteria for multipolaron formation are discussed.