Mapping ground states to string-nets

          @misc{ scivideos_PIRSA:24050032,
            doi = {10.48660/24050032},
            url = {https://pirsa.org/24050032},
            author = {Ranard, Daniel},
            keywords = {Quantum Information},
            language = {en},
            title = {Mapping ground states to string-nets},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {may},
            note = {PIRSA:24050032 see, \url{https://scivideos.org/index.php/pirsa/24050032}}
          }
          

Abstract

Two gapped ground states of lattice Hamiltonians are in the same quantum phase of matter, or topological phase, if they can be connected by a constant-depth circuit. It is conjectured that in two spatial dimensions, two gapped ground states with gappable boundary are in the same phase if and only if they have the same anyon contents, which are described by a unitary modular tensor category. We prove this conjecture for a class of states that obey a strict form of area law. Our main technical development is to transform these states into string-net wavefunctions using constant-depth circuits.