Interacting chiral fermions on the lattice with matrix product operator norms

• URL: http://arxiv.org/abs/2405.10285v2
• Date: Tue, 4 Jun 2024 00:01:16 GMT
• Title: Interacting chiral fermions on the lattice with matrix product operator norms
• Authors: Jutho Haegeman, Laurens Lootens, Quinten Mortier, Alexander Stottmeister, Atsushi Ueda, Frank Verstraete,
• Abstract summary: We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice. The fermion doubling problem is circumvented by constructing a Fock space endowed with a semi-definite norm. We demonstrate that the scaling limit of the free model recovers the chiral fermion field.
• Score: 37.69303106863453
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice while preserving unitarity and locality and without breaking the chiral symmetry. The fermion doubling problem is circumvented by constructing a Fock space endowed with a semi-definite norm. When projecting our theory on the the single-particle sector, we recover the framework of Stacey fermions, and we demonstrate that the scaling limit of the free model recovers the chiral fermion field. Technically, we make use of a matrix product operator norm to mimick the boundary of a higher dimensional topological theory. 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 to demonstrate that the ground state for large system sizes can be determined efficiently. As our tensor network approach does not exhibit any sign problem, we can add a chemical potential and study real-time evolution.

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