  We develop a variational scheme called "Gutzwiller renormalization group"
(GRG), which enables us to calculate the ground state of Anderson impurity
models (AIM) with arbitrary numerical precision. Our method can exploit the
low-entanglement property of the ground state in combination with the framework
of the Gutzwiller wavefunction, and suggests that the ground state of the AIM
has a very simple structure, which can be represented very accurately in terms
of a surprisingly small number of variational parameters. We perform benchmark
calculations of the single-band AIM that validate our theory and indicate that
the GRG might enable us to study complex systems beyond the reach of the other
methods presently available and pave the way to interesting generalizations,
e.g., to nonequilibrium transport in nanostructures.
