  Lattice regularization of chiral fermions has been a long-standing problem in
physics. In this work, we present the density matrix renormalization group
(DMRG) simulation of the 3-4-5-0 model of (1+1)D chiral fermions with an
anomaly-free chiral U(1) symmetry, which contains two left-moving and two
right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively.
Following the Wang-Wen chiral fermion model, we realize the chiral fermions and
their mirror partners on the opposite boundaries of a thin strip of (2+1)D
lattice model of multi-layer Chern insulator, whose finite-width implies the
quantum system is effectively (1+1)D. By introducing carefully designed two
sets of six-fermion local interactions to the mirror sector only, we
demonstrate that the mirror fermions can be gapped out by the interaction
beyond a critical strength without breaking the chiral U(1) symmetry, via the
symmetric mass generation (SMG) mechanism. We show that the interaction-driven
gapping transition is in the Berezinskii-Kosterlitz-Thouless (BKT) universality
class. We determine the evolution of Luttinger parameters before the
transition, which confirms that the transition happens exactly at the point
when the interaction term becomes marginal. As the mirror sector is gapped
after the transition, we check that the fermions in the light chiral fermion
sector remain gapless, which provides the desired lattice regularization of
chiral fermions.
