  The Luttinger model is a paradigm for the breakdown due to interactions of
the Fermi liquid description of one-dimensional massless Dirac fermions.
Attempts to discretize the model on a one-dimensional lattice have failed to
reproduce the established bosonization results, because of the fermion-doubling
obstruction: A local and symmetry-preserving discretization of the Hamiltonian
introduces a spurious second species of low-energy excitations, while a
nonlocal discretization opens a single-particle gap at the Dirac point. Here we
show how to work around this obstruction, by discretizing both space and time
to obtain a \textit{local} Lagrangian for a helical Luttinger liquid with
Hubbard interaction. The approach enables quantum Monte Carlo simulations that
preserve the topological protection of an unpaired Dirac cone.
