Ground state of a general electron-phonon Hamiltonian is a spin singlet
Abstract
The many-body ground state of a very general class of electron-phonon Hamiltonians is proven to contain a spin singlet (for an even number of electrons on a finite lattice). The phonons interact with the electronic system in two different ways; there is an interaction with the local electronic charge and there is a functional dependence of the electronic hopping Hamiltonian on the phonon coordinates. The phonon potential energy may include anharmonic terms, and the electron-phonon couplings and the hopping matrix elements may be nonlinear functions of the phonon coordinates. An attractive Hubbard-type on-site interaction may also be added. If the hopping Hamiltonian is assumed to have no phonon-coordinate dependence, then the ground state of a finite system is also shown to be unique, implying that there are no ground-state level crossings, and that the ground-state energy is an analytic function of the parameters in the Hamiltonian. In particular, in a finite system any self-trapping transition is a smooth crossover not accompanied by a nonanalytical change in the ground state. The spin-singlet theorem applies to the Su-Schrieffer-Heeger model and both the spin-singlet and uniqueness theorems apply to the Holstein and attractive Hubbard models as special cases. These results hold in all dimensions-even on a general graph without periodic lattice structure.
- Publication:
-
Physical Review B
- Pub Date:
- February 1995
- DOI:
- 10.1103/PhysRevB.51.2812
- arXiv:
- arXiv:cond-mat/9407026
- Bibcode:
- 1995PhRvB..51.2812F
- Keywords:
-
- 71.38.+i;
- 63.20.Kr;
- 74.20.-z;
- 75.10.Lp;
- Phonon-electron and phonon-phonon interactions;
- Theories and models of superconducting state;
- Band and itinerant models;
- Condensed Matter
- E-Print:
- 25 pages, no figures, plaintex