Perfect Lattice Topology: The Quantum Rotor as a Test Case

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.

12 pages, including two figures. ordinary LaTeX, requires fps.sty; Submitted to Phys. Lett. B

Cited by in corpus (18)

• Topological Lattice Actions
• Overlap Hypercube Fermions in QCD Simulations Near the Chiral Limit
• Measuring the Topological Susceptibility in a Fixed Sector
• Interpreting Numerical Measurements in Fixed Topological Sectors
• Theta-vacuum: Phase Transitions and/or Symmetry Breaking at $\theta =\pi$
• Topological Susceptibility from Slabs
• Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model
• Optimised Dirac Operators on the Lattice: Construction, Properties and Applications
• Perfect Lattice Perturbation Theory: A Study of the Anharmonic Oscillator
• Strong CP problem in the quantum rotor
• Topological Susceptibility of the 2d O(3) Model under Gradient Flow
• Blocking of lattice monopoles from the continuum in hot lattice gluodynamics
• Spin chain simulations with a meron cluster algorithm
• Instanton Density Operator in Lattice QCD from Higher Category Theory
• Topological Susceptibility under Gradient Flow
• Homotopy data as part of the lattice field: A first study
• Hamiltonian Lattice Formulation of Compact Maxwell-Chern-Simons Theory
• Lattice meets lattice: Application of lattice cubature to models in lattice gauge theory