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We discuss the general theoretical arguments advanced earlier for the T=0global phase diagram of antiferromagnetic Kondo lattice systems, distinguishingbetween the established and the conjectured. In addition to the well-knownphase of a paramagnetic metal with a "large" Fermi surface (P_L), there is alsoan antiferromagnetic phase with a "small" Fermi surface (AF_S). We provide thedetails of the derivation of a quantum non-linear sigma-model (QNLsM)representation of the Kondo lattice Hamiltonian, which leads to an effectivefield theory containing both low-energy fermions in the vicinity of a Fermisurface and low-energy bosons near zero momentum. An asymptotically exactanalysis of this effective field theory is made possible through thedevelopment of a renormalization group procedure for mixed fermion-bosonsystems. Considerations on how to connect the AF_S and P_L phases lead to aglobal phase diagram, which not only puts into perspective the theory of localquantum criticality for antiferromagnetic heavy fermion metals, but alsoprovides the basis to understand the surprising recent experiments inchemically-doped as well as pressurized YbRh2Si2. We point out that the AF_Sphase still occurs for the case of an equal number of spin-1/2 local momentsand conduction electrons. This observation raises the prospect for a globalphase diagram of heavy fermion systems in the Kondo-insulator regime. Finally,we discuss the connection between the Kondo breakdown physics discussed herefor the Kondo lattice systems and the non-Fermi liquid behavior recentlystudied from a holographic perspective.

Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators