Interacting chiral fermions on the lattice with matrix product operator norms
arxiv(2024)
Abstract
We develop a formalism for simulating one-dimensional interacting chiral
fermions on the lattice without breaking any local symmetries by defining a
Fock space endowed with a semi-definite norm defined in terms of matrix product
operators. This formalism can be understood as a second-quantized form of
Stacey fermions, hence providing a possible solution for the fermion doubling
problem and circumventing the Nielsen-Ninomiya theorem. We prove that the
emerging theory is hermitian by virtue of the fact that it gives rise to a
hermitian generalized eigenvalue problem and that it has local features as it
can be simulated using tensor network methods similar to the ones used for
simulating local quantum Hamiltonians. We also show that the scaling limit of
the free model recovers the chiral fermion field. As a proof of principle, we
consider a single Weyl fermion on a periodic ring with Hubbard-type
nearest-neighbor interactions and construct a variational generalized DMRG code
demonstrating that the ground states of the system for large system sizes can
be determined efficiently.
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