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 W_eff/W₀ (W₀/εF{)}^{{α}/1{{-}}{α}}$, where {α} measures the coupling strength between particle and environment. A renormalization-group analysis gives the same result for {α}<1 and an effective bandwidth Weff=0 for {α}>1, indicating a (zero temperature) localization transition.