Abstract:
Lattice actions and topological charges that are classically
and quantum mechanically perfect (i.e. free of lattice
artifacts) are constructed analytically for the quantum
rotor. It is demonstrated that the Manton action is
classically perfect while the Villain action is quantum
perfect. The geometric construction for the topological
charge is only perfect at the classical level. The quantum
perfect lattice topology associates a topological charge
distribution, not just a single charge, with each lattice
field configuration. For the quantum rotor with the
classically perfect action and topological charge, the
remaining cut-off effects are exponentially suppressed.