  A large class of quantum phase transitions for quantum lattice systems are
characterized by local order parameters. It is shown that local order
parameters may be systematically constructed from tensor network
representations of quantum many-body ground state wave functions by
investigating the reduced density matrices for local areas on an infinite-size
lattice. Depending on whether or not the system symmetries are spontaneously
broken, and whether or not the ground state fidelity per lattice site is
continuous, there are four categories of quantum phase transitions for systems
with local order parameters. Quantum phase transitions characterized by
nonlocal order parameters are discussed, aiming at better understanding quantum
systems with topological order.
