Interacting chiral fermions on the lattice with matrix product operator norms
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arXiv
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| Format: | Preprint |
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2024
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| author | Haegeman, Jutho Lootens, Laurens Mortier, Quinten Stottmeister, Alexander Ueda, Atsushi Verstraete, Frank |
| author_facet | Haegeman, Jutho Lootens, Laurens Mortier, Quinten Stottmeister, Alexander Ueda, Atsushi Verstraete, Frank |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10285 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interacting chiral fermions on the lattice with matrix product operator norms Haegeman, Jutho Lootens, Laurens Mortier, Quinten Stottmeister, Alexander Ueda, Atsushi Verstraete, Frank High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics 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. |
| title | Interacting chiral fermions on the lattice with matrix product operator norms |
| topic | High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2405.10285 |