From an insulating to a superfluid pair-bond liquid

We study an exchange coupled system of itinerant electrons and localized fermion pairs resulting in a resonant pairing formation. This system inherently contains resonating fermion pairs on bonds that lead to a superconducting phase, provided that long-range phase coherence between their constituents can be established. The prerequisite is that the resonating fermion pairs can become itinerant. This is rendered possible through the emergence of two kinds of bond fermions: individual and composite fermions made of one individual electron attached to a bound pair on a bond. If the strength of the exchange coupling exceeds a certain value, then the superconducting ground state undergoes a quantum phase transition into an insulating pair-bond liquid state. The gap of the superfluid phase thereby goes over continuously into a charge gap of the insulator. The changeover from the superconducting to the insulating phase is accompanied by a corresponding qualitative modification of the dispersion of the two kinds of fermionic excitations. Using a bond operator formalism, we derive the phase diagram of such a scenario together with the elementary excitations characterizing the various phases as a function of the exchange coupling and the temperature.