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arXiv · 2306.10105

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

Lukasz Fidkowski·Cenke Xu
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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 $2N$.

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Lukasz Fidkowski, Cenke Xu. 2023-06-16. A no-go result for implementing chiral symmetries by locality-preserving unitaries in a 3 dimensional Hamiltonian lattice model of fermions. https://doi.org/10.1103/physrevlett.131.196601

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