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A no-go result for implementing chiral symmetries by locality-preserving unitaries in a 3 dimensional Hamiltonian lattice model of fermions
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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 $2N$.
Forward citations
Cited by 2 Pith papers
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Fermionic Villain model with exact lattice chiral symmetries
A fermionic Villain lattice Hamiltonian exactly realizes the chiral U(1) L x U(1) R symmetry and anomalies of a massless Dirac fermion, enabling exact studies of symmetric mass generation and chiral lattice gauge theories.
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Ginsparg-Wilson Hamiltonians with Improved Chiral Symmetry
A tunable family of Ginsparg-Wilson Hamiltonians is constructed in which the chiral charge becomes progressively more quantized as k increases, though locality degrades.
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