



01749nas a2200169   4500008004100000245009500041210006900136260001400205520115200219653002701371653003101398653005201429100001701481700002101498700002301519856003701542       2022                        eng d00aExtracting Wilson loop operators and fractional statistics from a single bulk ground state0 aExtracting Wilson loop operators and fractional statistics from   c9/28/20223 a<p>An essential aspect of topological phases of matter is the existence of Wilson loop operators that keep the ground state subspace invariant. Here we present and implement an unbiased numerical optimization scheme to systematically find the Wilson loop operators given a single ground state wave function of a gapped Hamiltonian on a disk. We then show how these Wilson loop operators can be cut and glued through further optimization to give operators that can create, move, and annihilate anyon excitations. We subsequently use these operators to determine the braiding statistics and topological twists of the anyons, yielding a way to fully extract topological order from a single wave function. We apply our method to the ground state of the perturbed toric code and doubled semion models with a magnetic field that is up to a half of the critical value. From a contemporary perspective, this can be thought of as a machine learning approach to discover emergent 1-form symmetries of a ground state wave function. From an application perspective, our approach can be relevant to find Wilson loop operators in current quantum simulators.</p>10aFOS: Physical sciences10aQuantum Physics (quant-ph)10aStrongly Correlated Electrons (cond-mat.str-el)1 aCian, Ze-Pei1 aHafezi, Mohammad1 aBarkeshli, Maissam  uhttps://arxiv.org/abs/2209.14302