Digitizing lattice gauge theories in the magnetic basis: reducing the breaking of the fundamental commutation relations

Abstract

Abstract We present a digitization scheme for the lattice $${\textrm{SU}}(2)$$ SU ( 2 ) gauge theory Hamiltonian in the magnetic basis, where the gauge links are unitary and diagonal. The digitization is obtained from a particular partitioning of the $${\textrm{SU}}(2)$$ SU ( 2 ) group manifold, with the canonical momenta constructed by an approximation of the Lie derivatives on this partitioning. This construction, analogous to a discrete Fourier transform, preserves the spectrum of the electric part of the Hamiltonian and the canonical commutation relations exactly on a subspace of the truncated Hilbert space, while the residual subspace can be projected above the cutoff of the theory.