PIRSA:25110079

Locality Preserving Unitaries Beyond QCA

Zhang, C. (2025). Locality Preserving Unitaries Beyond QCA. Perimeter Institute. https://pirsa.org/25110079

Zhang, Carolyn. Locality Preserving Unitaries Beyond QCA. Perimeter Institute, Nov. 12, 2025, https://pirsa.org/25110079 

          @misc{ pirsa_PIRSA:25110079,
            doi = {},
            url = {https://pirsa.org/25110079},
            author = {Zhang, Carolyn},
            keywords = {Condensed Matter},
            language = {en},
            title = {Locality Preserving Unitaries Beyond QCA},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {nov},
            note = {PIRSA:25110079 see, \url{https://pirsa.org}}
          }

Carolyn Zhang Harvard University

Talk numberPIRSA:25110079
Collection
Talk Type Other
Subject

Abstract

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.