A No-Go Result for Implementing Chiral Symmetries by Locality-Preserving Unitaries in a Three-Dimensional Hamiltonian Lattice Model of Fermions
Lukasz Fidkowski, Cenke Xu
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 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.
Topics & Concepts
FermionPhysicsHamiltonian (control theory)Homogeneous spaceMathematical physicsLattice (music)HelicityHilbert spaceQuantum mechanicsTheoretical physicsMathematicsGeometryAcousticsMathematical optimizationTopological Materials and PhenomenaQuantum many-body systemsQuantum and electron transport phenomena