  Quantum phase transitions (QPTs) arise as a result of competing interactions
in a quantum many-body system. Kondo lattice models, containing a lattice of
localized magnetic moments and a band of conduction electrons, naturally
feature such competing interactions. A Ruderman-Kittel-Kasuya-Yosida (RKKY)
exchange interaction among the local moments promotes magnetic ordering.
However, a Kondo exchange interaction between the local moments and conduction
electrons favors the Kondo-screened singlet ground state. This chapter
summarizes the basic physics of QPTs in antiferromagnetic Kondo lattice
systems. Two types of quantum critical points (QCPs) are considered.
Spin-density-wave quantum criticality occurs at a conventional type of QCP,
which invokes only the fluctuations of the antiferromagnetic order parameter.
Local quantum criticality describes a new type of QCP, which goes beyond the
Landau paradigm and involves a breakdown of the Kondo effect. This critical
Kondo breakdown effect leads to non-Fermi liquid electronic excitations, which
are part of the critical excitation spectrum and are in addition to the
fluctuations of the magnetic order parameter. Across such a QCP, there is a
sudden collapse of the Fermi surface from large to small. I close with a brief
summary of relevant experiments, and outline a number of outstanding issues,
including the global phase diagram.
