Topology and stability of the Kondo phase in quark matter

Abstract

We investigate properties of the ground state of a light quark matter with heavy quark impurities. This system exhibits the "QCD Kondo effect" where the interaction strength between a light quark near the Fermi surface and a heavy quark increases with decreasing energy of the light quark towards the Fermi energy, and diverges at some scale near the Fermi energy, called the Kondo scale. Around and below the Kondo scale, we must treat the dynamics nonperturbatively. As a typical nonperturbative method to treat the strong coupling regime, we adopt a mean-field approach where we introduce a condensate, the Kondo condensate, representing a mixing between a light quark and a heavy quark, and determine the ground state in the presence of the Kondo condensate. We show that the ground state is a topologically non-trivial state and the heavy quark spin forms the hedgehog configuration in the momentum space. We can define the Berry phase for the ground-state wavefunction in the momentum space which is associated with a monopole at the position of a heavy quark. We also investigate fluctuations around the mean field in the random-phase approximation, and show the existence of (exciton-like) collective excitations made of a hole $h$ of a light quark and a heavy quark $Q$.