Gauge symmetry of excited states in projected entangled-pair state simulations

While gauge symmetry is a well-established requirement for representing topological orders in projected entangled-pair state (PEPS), its impact on the properties of low-lying excited states remains relatively unexplored. Here we perform PEPS simulations of low-energy dynamics in the Kitaev honeycomb model, which supports fractionalized gauge flux (vison) excitations. We identify gauge symmetry emerging upon optimizing an unbiased PEPS ground state. Using the PEPS adapted local mode approximation, we further classify the low-lying excited states by discerning different vison sectors. Our simulations of spin and spin-dimer dynamical correlations establish close connections with experimental observations. Notably, the selection rule imposed by the locally conserved visons results in nearly flat dispersions in momentum space for excited states belonging to the 2-vison or 4-vison sectors.