Low-temperature properties of a two-level system interacting with conduction electrons: An application of the overcompensated multichannel Kondo model

We consider an atom in a double-well potential [parametrized by a two-level system (TLS)] interacting with screened conduction electrons. The tunneling of the TLS is assisted by the Fermi gas. Close to the strong-coupling fixed point the renormalization-group equations for the noncommutative model in the case of spinless fermions, but an arbitrary number of relevant orbital channels, lead to the n-channel Kondo problem with S=1/2. By solving the thermodynamic Bethe-ansatz equations for the n-channel Kondo problem numerically in the presence of a magnetic field, we discuss the low-temperature properties of the TLS close to the fixed point. The Zeeman splitting corresponds to the energy difference between the two positions of the tunneling atom. The atom is not localized at one of the potential minima. The susceptibility diverges as H→0 and T→0, indicating that the symmetric TLS is unstable against a local lattice deformation via coupling to phonons. The lattice distortion disappears above a critical temperature ${\mathit{T}}_{\mathit{c}}$. The ground-state equilibrium situation of the TLS corresponds to H≠0 and a Fermi-liquid picture applies. The values for the specific heat become very large as H→0. For small fields the specific heat shows a double-peak structure, which is particularly pronounced for n=2.