Tunable Non-Fermi Liquid Phase from Coupling to Two-Level Systems

We study a controlled large-N theory of electrons coupled to dynamical two-level systems (TLSs) via spatially random interactions. Such a physical situation arises when electrons scatter off low-energy excitations in a metallic glass, such as a charge or stripe glass. Our theory is governed by a non-Gaussian saddle point, which maps to the celebrated spin-boson model. By tuning the coupling strength we find that the model crosses over from a Fermi liquid at weak coupling to an extended region of non-Fermi liquid behavior at strong coupling, and realizes a marginal Fermi liquid at the crossover. Our results are valid for generic space dimensions d>1.