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U(1) x U(1) SPT in Gutzwiller-projected parton wave functions and its possible realization in a local spin model

Gutzwiller projection is a way to construct many-body wave functions that could carry topological order or symmetry protected topological (SPT) order. However, an important issue is to determine whether a given Gutzwiller-projected wave functions (GPWF) carries a non-trivial SPT order or not, and which SPT order is carried by the wavefunction. In this paper, we numerically study the SPT order in a spin S=1 GPWF on the Kagome lattice. Using the standard Monte Carlo method, we directly confirm that the GPWF has (1) gapped bulk with short-range correlations, (2) a trivial topological order via non degenerate ground state, and zero topological entanglement entropy, (3) a non-trivial U(1)×U(1) SPT order via the Hall conductances of the protecting U(1)×U(1) symmetry, (4) symmetry protected gapless boundary. The possible realization of the PST order is also proposed in a local S = 1 spin model.