Multi-scale Quantum Criticality driven by Kondo-lattice Coupling in Pyrochlore Systems

Pyrochlore systems with local moments and 5d conduction electrons offer excellent material platforms for the discovery of exotic quantum many-body ground states. Notable examples include U(1) quantum spin liquid (QSL) and semimetallic non-Fermi liquid state. Here we investigate emergent quantum phases and their transitions driven by the Kondo-lattice couplings. Using the renormalization group method, we show that weak Kondo-lattice coupling is irrelevant, leading to a fractionalized semimetal phase with decoupled local moments and conduction electrons. Upon increasing the Kondo-lattice coupling, this phase is unstable to the formation of broken symmetry states. The important thing is the opposing influence of the Kondo-lattice coupling and long-range Coulomb interaction. The former prefers to break the particle-hole symmetry while the latter tends to restore it. The characteristic competition leads to multiple phase transitions, first from a fractionalized semimetal phase to a fractionalized Fermi surface state with particle-hole pockets, followed by the second transition to a fractionalized ferromagnetic state. Multi-scale quantum critical behaviors appear at non-zero temperatures and with the external magnetic field near such quantum phase transitions.