A no-go result for implementing chiral symmetries by locality-preserving unitaries in a 3 dimensional Hamiltonian lattice model of fermions

Abstract

We argue that the chiral $U(1{)}_A$ symmetry of a Weyl fermion cannot be implemented by a shallow depth quantum circuit operation in a fermionic lattice Hamiltonian model with finite dimensional onsite Hilbert spaces. We also extend this result to discrete ${\mathbb{Z}}_{2N}$ subgroups of $U(1{)}_A$, in which case we show that for $N_f$ Weyl fermions of the same helicity, this group action cannot be implemented with shallow depth circuits when $N_f$ is not an integer multiple of $2N$.

3 figures, v3 typo fixed

References in corpus (5)

• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Interacting Topological Insulator and Emergent Grand Unified Theory
• Comments on Symmetric Mass Generation in 2d and 4d
• Gapped Chiral Fermions
• 't Hooft anomalies for staggered fermions

Cited by in corpus (4)

• Exact Chiral Symmetries of 3+1D Hamiltonian Lattice Fermions
• Minimal-doubling and single-Weyl Hamiltonians
• Boundary topological orders of (4+1)d fermionic ${\mathbb{Z}}_{2N}^{\mathrm{F}}$ SPT states
• Equivalence class of Emergent Single Weyl fermion lattice models in 3 dimensions: gapless superconductors and superfluids versus chiral fermions