Locality Preserving Unitaries Beyond QCAConfirmed

by Carolyn Zhang (Harvard University)

Wednesday Nov 12, 2025, 3:30 PM → 5:00 PM America/Toronto

PI/4-405 - Bob Room (Perimeter Institute for Theoretical Physics)

We study a locality preserving unitary (LPU) in three spatial dimensions that “pumps” a Chern insulator to the physical boundary. In the single-particle setting, the LPU cannot be generated by any local Hamiltonian. However, it is not a quantum cellular automaton (QCA) because it transforms strictly local operators into operators with exponentially decaying tails. In the fermionic many-body setting, the LPU can be generated by a local Hamiltonian, but the Hamiltonian must break the U (1) symmetry generated by total particle number. It is therefore an LPU “protected” by U (1) symmetry. We identify an integer valued topological invariant for the LPU. We also obtain ZN LPUs for N even and N > 2, from breaking the U (1) symmetry down to ZN. To our knowledge, this is the first example of an LPU that transforms strictly local operators into operators with

exponential tails and cannot be realized as a QCA.