Static properties of a particle coupled to a fermionic environment

We study the ground-state properties of a particle moving in a tight-binding band and coupled to a Fermi sea of metal electrons. Using an effective Hamiltonian and a variational ground state, we find a band narrowing of Weff/W0 (W0/EF)±/1-±, where ± measures the coupling strength between particle and environment. A renormalization-group analysis gives the same result for ±<1 and an effective bandwidth Weff=0 for ±>1, indicating a (zero temperature) localization transition. © 1987 The American Physical Society.