Ground-state energy of a two level system with phonon coupling

The coupling of a two-level system to quantized boson modes has been the focus of many researchers for a number of years. Applications to exciton motion, molecular polaron formation, chaos in quantum systems as well as a number of other effects in condensed matter physics have also been studied. Here we investigate the interaction of bosonic modes with a two-level fermionic system. This quantum system is used as a testing ground for a recently developed Generalized Moments Expansion, GMX(m,n), of which the well-known Connected Moments Expansion (CMX) and Alternate Moments Expansion (AMX) are special cases. The convergence and viability of this scheme are discussed and comparisons are made with a related Canonical Sequence Method (CSM) as well as a Lanczos tridiagonal truncation scheme.