Interacting chiral fermions on the lattice with matrix product operator norms

TL;DR

This paper introduces a Hamiltonian formalism using matrix product operator norms to simulate interacting chiral fermions on the lattice, preserving key symmetries and avoiding fermion doubling, with efficient numerical methods demonstrated.

Contribution

It presents a novel tensor network approach with a semi-definite norm to simulate chiral fermions, maintaining unitarity and locality without symmetry breaking.

Findings

Successfully simulates a single Weyl fermion with interactions

Recovers chiral fermion field in the scaling limit

Efficiently determines ground states for large systems

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.